{"id":4618,"date":"2022-01-14T21:01:50","date_gmt":"2022-01-14T21:01:50","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=4618"},"modified":"2022-02-08T19:00:03","modified_gmt":"2022-02-08T19:00:03","slug":"clase-digital-5-funcion-inversa-funcion-implicita-otro-tipo-de-funciones-par-impar-y-transformada","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-5-funcion-inversa-funcion-implicita-otro-tipo-de-funciones-par-impar-y-transformada\/","title":{"rendered":"Clase digital 5: Funcio\u0301n inversa.  Funcio\u0301n impli\u0301cita. Otro tipo de funciones (par, impar y transformada)"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover is-light\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"has-background-dim-40 wp-block-cover__gradient-background has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-4606\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck.jpg\" style=\"object-position:59% 64%\" data-object-fit=\"cover\" data-object-position=\"59% 64%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1067\" class=\"wp-block-cover__image-background wp-image-4606\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck.jpg\" style=\"object-position:59% 64%\" data-object-fit=\"cover\" data-object-position=\"59% 64%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck.jpg 1600w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck-300x200.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck-1024x683.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck-768x512.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck-1536x1024.jpg 1536w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/zsl306fdck-272x182.jpg 272w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><\/noscript><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-base-3-color has-text-color has-large-font-size wp-block-paragraph\">Funcio\u0301n inversa. Funcio\u0301n impli\u0301cita. Otro tipo de funciones (par, impar y transformada)<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"introduccion\">Introducci\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Hola!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Me siento muy feliz al saber que sigues aprovechando este curso de C\u00e1lculo Diferencial, espero que lo sigas disfrutando, por lo tanto, te invito a comenzar nuestra quinta clase con los temas FUNCIO\u0301N INVERSA, FUNCIO\u0301N IMPLI\u0301CITA.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En la clase 3, se dio a conocer el concepto de una funci\u00f3n, en el cual la regla de correspondencia es la m\u00e1s importante para definir una funci\u00f3n, esta regla de correspondencia indica que a cada valor de x en su dominio X se asigna un solo valor o un valor \u00fanico y en su rango. Esta regla no excluye el hecho de que el mismo n\u00famero y se asocie con varios valores de x.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si se quisieran determinar los elementos de entrada se presentar\u00eda un inconveniente debido a que, para el elemento de salida a B, existen dos valores en el conjunto A para los cuales se cumple que f(x)=a estos son x=2 y x=6, lo cual se debe a que la relaci\u00f3n entre los conjuntos A y B no es uno a uno, la funci\u00f3n es no inyectiva<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Y es por ello, que se deben definir las funciones inversas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En relaci\u00f3n con lo anterior, te invito a proseguir. \u00a1\u00c9xito!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema<\/h2>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"funcion-inversa\">Funci\u00f3n inversa<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Se dice que una funcio\u0301n es uno a uno si cada nu\u0301mero en el rango de <em>f<\/em> se asocia con exactamente un nu\u0301mero en su dominio <em>X<\/em>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sea f una funci\u00f3n inyectiva con dominio A y contradominio B, se define a su funci\u00f3n inversa f-1 con dominio en B y contradominio en A como:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM1.png\" alt=\"\" class=\"wp-image-4885\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"313\" height=\"102\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM1.png\" alt=\"\" class=\"wp-image-4885\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM1.png 313w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM1-300x98.png 300w\" sizes=\"auto, (max-width: 313px) 100vw, 313px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Si y s\u00f3lo si <em>f(x) = y<\/em> para toda <em>x\u2208B<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Propiedades de la funci\u00f3n inversa:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Dominio de <em>f<sup>-1<\/sup><\/em>= rango de <em>f<\/em><\/li><li>Rango de <em>f<sup>-1<\/sup><\/em>= dominio de <em>f<\/em><\/li><li>Una funci\u00f3n inversa f-1 es uno a uno<\/li><li>La inversa de <em>f<sup>-1<\/sup><\/em> es <em>f<\/em><\/li><li>La inversa de f es \u00fanica.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Proceso para encontrar una funci\u00f3n inversa:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Verificar que la funci\u00f3n sea inyectiva, en caso de no serlo restringir el dominio donde la funci\u00f3n sea inyectiva (funci\u00f3n uno a uno)<\/li><li>Sustituir <em>f(x)<\/em> por <em>y<\/em><\/li><li>Despejar la variable <em>x<\/em><\/li><li>Intercambiar <em>x<\/em> por <em>y<\/em> y <em>y<\/em> por <em>x<\/em><\/li><li>El intercambio es la funci\u00f3n inversa y se escribe como <em>f<sup>-1<\/sup>(x)<\/em><\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Determina la funci\u00f3n inversa de<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM2.png\" alt=\"\" class=\"wp-image-4886\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"303\" height=\"108\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM2.png\" alt=\"\" class=\"wp-image-4886\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM2.png 303w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM2-300x107.png 300w\" sizes=\"auto, (max-width: 303px) 100vw, 303px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">su dominio y rango.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Soluci\u00f3n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Verificando que la funci\u00f3n sea inyectiva es decir uno a uno (recuerda puedes graficar para asegurarte)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La funci\u00f3n <em>f(x)<\/em> es inyectiva en su dominio de<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM3.png\" alt=\"\" class=\"wp-image-4887\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"598\" height=\"114\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM3.png\" alt=\"\" class=\"wp-image-4887\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM3.png 598w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM3-300x57.png 300w\" sizes=\"auto, (max-width: 598px) 100vw, 598px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Sustituyendo <em>f(x)<\/em> por <em>y<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM4.png\" alt=\"\" class=\"wp-image-4888\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"249\" height=\"132\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM4.png\" alt=\"\" class=\"wp-image-4888\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Despejando <em>x<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM5.png\" alt=\"\" class=\"wp-image-4889\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"506\" height=\"149\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM5.png\" alt=\"\" class=\"wp-image-4889\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM5.png 506w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM5-300x88.png 300w\" sizes=\"auto, (max-width: 506px) 100vw, 506px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Factorizando <em>x<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM6.png\" alt=\"\" class=\"wp-image-4890\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"607\" height=\"173\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM6.png\" alt=\"\" class=\"wp-image-4890\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM6.png 607w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM6-300x86.png 300w\" sizes=\"auto, (max-width: 607px) 100vw, 607px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Factorizando y dividiendo -1<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM7.png\" alt=\"\" class=\"wp-image-4891\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"252\" height=\"120\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM7.png\" alt=\"\" class=\"wp-image-4891\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Cambiando <em>x<\/em> por <em>y<\/em> y <em>y<\/em> por <em>x<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM8.png\" alt=\"\" class=\"wp-image-4892\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"260\" height=\"126\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM8.png\" alt=\"\" class=\"wp-image-4892\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Escribiendo como funci\u00f3n inversa<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM9.png\" alt=\"\" class=\"wp-image-4893\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"380\" height=\"135\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM9.png\" alt=\"\" class=\"wp-image-4893\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM9.png 380w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM9-300x107.png 300w\" sizes=\"auto, (max-width: 380px) 100vw, 380px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Encontrando el dominio de la funci\u00f3n inversa, como es una funci\u00f3n polinomial solo se considera el polinomio q(x) por tanto, el dominio de la funci\u00f3n es<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM10.png\" alt=\"\" class=\"wp-image-4894\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"452\" height=\"123\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM10.png\" alt=\"\" class=\"wp-image-4894\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM10.png 452w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM10-300x82.png 300w\" sizes=\"auto, (max-width: 452px) 100vw, 452px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">y por la propiedad 1 el rango es<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM11.png\" alt=\"\" class=\"wp-image-4895\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"402\" height=\"122\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM11.png\" alt=\"\" class=\"wp-image-4895\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM11.png 402w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM11-300x91.png 300w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">En la imagen que se presenta a continuaci\u00f3n se observa que se cumplen las propiedades 1 y 2 de las funciones inversas. La l\u00ednea azul representa la funci\u00f3n y la l\u00ednea roja representa la funci\u00f3n inversa.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM12.png\" alt=\"\" class=\"wp-image-4896\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"459\" height=\"466\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM12.png\" alt=\"\" class=\"wp-image-4896\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM12.png 459w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM12-295x300.png 295w\" sizes=\"auto, (max-width: 459px) 100vw, 459px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Encuentra la funci\u00f3n inversa de <em>f(x) = 5x &#8211; 7<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Soluci\u00f3n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La funci\u00f3n es una funci\u00f3n polinomial y lineal por lo tanto es una funci\u00f3n inyectiva cuyo dominio y rango es el conjunto de los n\u00fameros reales.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Calculando la funci\u00f3n inversa, despejando <em>x<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM13.png\" alt=\"\" class=\"wp-image-4897\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"158\" height=\"149\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM13.png\" alt=\"\" class=\"wp-image-4897\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Cambio de variables y escritura de la funci\u00f3n inversa.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM14.png\" alt=\"\" class=\"wp-image-4898\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"203\" height=\"84\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM14.png\" alt=\"\" class=\"wp-image-4898\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">La imagen muestra la funci\u00f3n y la funci\u00f3n inversa, la l\u00ednea gris es la funci\u00f3n <em>f(x) = 5x &#8211; 7<\/em> y la l\u00ednea verde representa la funci\u00f3n inversa<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM15.png\" alt=\"\" class=\"wp-image-4899\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"333\" height=\"94\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM15.png\" alt=\"\" class=\"wp-image-4899\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM15.png 333w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM15-300x85.png 300w\" sizes=\"auto, (max-width: 333px) 100vw, 333px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">se observa que el dominio y el rango de ambas funciones son todos los n\u00fameros reales y que se cumplen las propiedades 1 y 2.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM16.png\" alt=\"\" class=\"wp-image-4900\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"464\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM16.png\" alt=\"\" class=\"wp-image-4900\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM16.png 500w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM16-300x278.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"funcion-exponencial-y-logaritmica\">Funci\u00f3n exponencial y logar\u00edtmica<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Si b &gt; 0 y b \u2260 1, entonces una funcio\u0301n exponencial <em>y = f(x)<\/em> es una funcio\u0301n de la forma <em>f(x) = b<sup>x<\/sup><\/em> . El nu\u0301mero b se denomina base y x se denomina exponente. El dominio de la funci\u00f3n exponencial es el conjunto de los n\u00fameros reales.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"leyes-de-los-exponentes\">Leyes de los exponentes<\/h4>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM17-1024x183.png\" alt=\"\" class=\"wp-image-4901\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"183\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM17-1024x183.png\" alt=\"\" class=\"wp-image-4901\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM17-1024x183.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM17-300x54.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM17-768x137.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM17.png 1047w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">La funci\u00f3n logar\u00edtmica con base b &gt; 0 y b \u2260 1, se define por <em>y = x<\/em> si y s\u00f3lo si <em>x = b<sup>y<\/sup><\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Leyes de los logaritmos<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para cualquier base b&gt;0 y b 1 y n\u00fameros enteros de M y N<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM18.png\" alt=\"\" class=\"wp-image-4902\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"920\" height=\"266\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM18.png\" alt=\"\" class=\"wp-image-4902\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM18.png 920w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM18-300x87.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM18-768x222.png 768w\" sizes=\"auto, (max-width: 920px) 100vw, 920px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Simplifique y escriba<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM19.png\" alt=\"\" class=\"wp-image-4903\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"546\" height=\"115\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM19.png\" alt=\"\" class=\"wp-image-4903\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM19.png 546w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM19-300x63.png 300w\" sizes=\"auto, (max-width: 546px) 100vw, 546px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">como un logaritmo \u00fanico<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Soluci\u00f3n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La ecuaci\u00f3n tiene la forma iii por tanto se reescribir\u00e1.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM20.png\" alt=\"\" class=\"wp-image-4904\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"510\" height=\"110\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM20.png\" alt=\"\" class=\"wp-image-4904\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM20.png 510w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM20-300x65.png 300w\" sizes=\"auto, (max-width: 510px) 100vw, 510px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Realizando las operaciones<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM21.png\" alt=\"\" class=\"wp-image-4905\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"514\" height=\"95\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM21.png\" alt=\"\" class=\"wp-image-4905\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM21.png 514w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM21-300x55.png 300w\" sizes=\"auto, (max-width: 514px) 100vw, 514px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Utilizando la propiedad <em>i<\/em>, se reescribe a<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM22.png\" alt=\"\" class=\"wp-image-4906\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"344\" height=\"95\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM22.png\" alt=\"\" class=\"wp-image-4906\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM22.png 344w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM22-300x83.png 300w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"de-las-palabras-a-funciones\">De las palabras a funciones<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Todos los problemas matem\u00e1ticos inician con una descripci\u00f3n verbal, lo cual debe traducirse a una funci\u00f3n, y es lo que trataremos con los ejemplos que se plantean a continuaci\u00f3n.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La suma de dos nu\u0301meros no negativos es 5. Exprese el producto de uno y el cuadrado del otro como una funcio\u0301n de uno de los nu\u0301meros.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Soluci\u00f3n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La primer parte del enunciado plantea que son dos n\u00fameros mayores que cero, lo que se puede escribir matem\u00e1ticamente como: <em>x \u2265 0<\/em> y <em>y \u2265 0<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Con esto se puede plantear <em>x + y = 5<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para expresar como el producto es una multiplicaci\u00f3n y elevar el otro al cuadrado <em>P = xy<sup>2<\/sup><\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Como se pide escribirlo en funci\u00f3n de otro hay de despejar y sustituir, en este caso se despejara y para obtener una funci\u00f3n de <em>x<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM23.png\" alt=\"\" class=\"wp-image-4907\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"451\" height=\"157\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM23.png\" alt=\"\" class=\"wp-image-4907\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM23.png 451w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM23-300x104.png 300w\" sizes=\"auto, (max-width: 451px) 100vw, 451px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Un \u00e1rbol se planta a 30 pies de la base de un poste que mide 25 pies de altura. Exprese la longitud de la sombra como una funci\u00f3n de la altura.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Soluci\u00f3n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Realiza el dibujo y utiliza el concepto de triangulo semejante para realizar el planteamiento de las ecuaciones.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM24.png\" alt=\"\" class=\"wp-image-4908\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"865\" height=\"306\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM24.png\" alt=\"\" class=\"wp-image-4908\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM24.png 865w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM24-300x106.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM24-768x272.png 768w\" sizes=\"auto, (max-width: 865px) 100vw, 865px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM25.png\" alt=\"\" class=\"wp-image-4909\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"277\" height=\"125\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM25.png\" alt=\"\" class=\"wp-image-4909\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exprese la distancia de un punto (<em>x, y<\/em>) en el primer cuadrante sobre el c\u00edrculos <em>x<sup>2<\/sup> + y<sup>2<\/sup> = 1<\/em> hasta el punto (2, 4) como una funci\u00f3n de <em>x<\/em>.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM26.png\" alt=\"\" class=\"wp-image-4910\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"717\" height=\"510\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM26.png\" alt=\"\" class=\"wp-image-4910\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM26.png 717w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM26-300x213.png 300w\" sizes=\"auto, (max-width: 717px) 100vw, 717px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM27.png\" alt=\"\" class=\"wp-image-4911\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"511\" height=\"426\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM27.png\" alt=\"\" class=\"wp-image-4911\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM27.png 511w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CD5_IM27-300x250.png 300w\" sizes=\"auto, (max-width: 511px) 100vw, 511px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">En conclusi\u00f3n, las funciones son ecuaciones que describen el comportamiento de predicciones de la vida real, recuerda que las funciones son modelos matem\u00e1ticos que predicen comportamientos en puntos dados.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Una funci\u00f3n tiene una variable dependiente y una independiente, lo que ayuda en las predicciones.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Es as\u00ed como se concluye esta quinta sesi\u00f3n. \u00a1Felicitaciones por tu esfuerzo y dedicaci\u00f3n! No olvides realizar y mandar en tiempo y forma tu tarea, hasta la pr\u00f3xima sesi\u00f3n.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"fuentes-de-informacion\">Fuentes de informaci\u00f3n<\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>Zill, D. G., &amp; Wrigth. W. S. (2011). Matem\u00e1ticas 1: C\u00e1lculo Diferencial. M\u00e9xico: MC Graw Hill.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n \u00a1Hola! Me siento muy feliz al saber que sigues aprovechando este curso de C\u00e1lculo Diferencial, espero que lo sigas disfrutando, por lo tanto, te invito a comenzar nuestra quinta clase con los temas FUNCIO\u0301N INVERSA, FUNCIO\u0301N IMPLI\u0301CITA. En la clase 3, se dio a conocer el concepto de una funci\u00f3n, en el cual la &#8230; <a title=\"Clase digital 5: Funcio\u0301n inversa.  Funcio\u0301n impli\u0301cita. Otro tipo de funciones (par, impar y transformada)\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-5-funcion-inversa-funcion-implicita-otro-tipo-de-funciones-par-impar-y-transformada\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 5: Funcio\u0301n inversa.  Funcio\u0301n impli\u0301cita. Otro tipo de funciones (par, impar y transformada)\">Leer m\u00e1s<\/a><\/p>\n","protected":false},"author":142,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","episode_type":"","audio_file":"","podmotor_file_id":"","podmotor_episode_id":"","cover_image":"","cover_image_id":"","duration":"","filesize":"","filesize_raw":"","date_recorded":"","explicit":"","block":"","itunes_episode_number":"","itunes_title":"","itunes_season_number":"","itunes_episode_type":"","footnotes":""},"categories":[10,12],"tags":[41,149,44],"class_list":["post-4618","post","type-post","status-publish","format-standard","hentry","category-ingenieria-civil","category-uda-calculo-diferencial","tag-clase-digital","tag-marcela-guadalupe-tellez-martinez","tag-neli04036"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/4618","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/users\/142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/comments?post=4618"}],"version-history":[{"count":5,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/4618\/revisions"}],"predecessor-version":[{"id":6960,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/4618\/revisions\/6960"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=4618"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=4618"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=4618"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}