{"id":1276,"date":"2025-09-18T17:43:38","date_gmt":"2025-09-18T23:43:38","guid":{"rendered":"https:\/\/portal.pronea.gt\/?p=1276"},"modified":"2025-09-18T17:47:36","modified_gmt":"2025-09-18T23:47:36","slug":"temporary-title-790-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2","status":"publish","type":"post","link":"https:\/\/portal.pronea.gt\/?p=1276","title":{"rendered":"Funci\u00f3n inversa y su gr\u00e1fica"},"content":{"rendered":"<div id=\"cmsmasters_row_\" class=\"cmsmasters_row cmsmasters_color_scheme_default cmsmasters_row_top_default cmsmasters_row_bot_default cmsmasters_row_boxed\">\n<div class=\"cmsmasters_row_outer_parent\">\n<div class=\"cmsmasters_row_outer\">\n<div class=\"cmsmasters_row_inner\">\n<div class=\"cmsmasters_row_margin\">\n<div id=\"cmsmasters_column_\" class=\"cmsmasters_column one_first\">\n<div class=\"cmsmasters_column_inner\"><div class=\"cmsmasters_text\" data-animation=\"fadeIn\">\n<p data-start=\"2106\" data-end=\"2337\">La <strong data-start=\"2109\" data-end=\"2128\">funci\u00f3n inversa<\/strong> es una herramienta matem\u00e1tica que nos permite &#8220;deshacer&#8221; el efecto de otra funci\u00f3n. Si una funci\u00f3n transforma una entrada <span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span> en una salida <span class=\"katex\"><span class=\"katex-mathml\">yy<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span>, la inversa hace el recorrido contrario: de <span class=\"katex\"><span class=\"katex-mathml\">yy<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span> a <span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span>.<\/p>\n<p data-start=\"2339\" data-end=\"2413\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f3a5.svg\" alt=\"\ud83c\udfa5\" \/> <strong data-start=\"2342\" data-end=\"2364\">Mira el video aqu\u00ed<\/strong><\/p>\n<iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/oqpGUFYzg3Y?si=8cU5rbqjYs875-wB\" width=\"1120\" height=\"630\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<hr data-start=\"2415\" data-end=\"2418\" \/>\n<h2 data-start=\"2420\" data-end=\"2456\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4cd.svg\" alt=\"\ud83d\udccd\" \/> \u00bfQu\u00e9 es una funci\u00f3n inversa?<\/h2>\n<p data-start=\"2457\" data-end=\"2508\">Una funci\u00f3n <span class=\"katex\"><span class=\"katex-mathml\">f(x)<\/span><\/span>\u00a0tiene inversa si cumple que:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1278\" src=\"https:\/\/portal.pronea.gt\/wp-content\/uploads\/2025\/09\/funcion_inversa1.png\" alt=\"Formula de la funci\u00f3n inversa\" width=\"189\" height=\"66\" \/><\/p>\n<p data-start=\"2534\" data-end=\"2616\">Es decir, aplicar una funci\u00f3n y luego su inversa nos devuelve el valor original.<\/p>\n<p data-start=\"2618\" data-end=\"2628\">Ejemplo:<\/p>\n<p data-start=\"2618\" data-end=\"2628\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1279\" src=\"https:\/\/portal.pronea.gt\/wp-content\/uploads\/2025\/09\/funcion_inversa2.png\" alt=\"F\u00f3rmula de la funci\u00f3n inversa\" width=\"548\" height=\"116\" \/><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<hr data-start=\"2704\" data-end=\"2707\" \/>\n<h2 data-start=\"2709\" data-end=\"2749\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4c8.svg\" alt=\"\ud83d\udcc8\" \/> La gr\u00e1fica de la funci\u00f3n inversa<\/h2>\n<p data-start=\"2750\" data-end=\"2840\">La representaci\u00f3n gr\u00e1fica de una funci\u00f3n y su inversa tiene una caracter\u00edstica especial:<\/p>\n<ul data-start=\"2841\" data-end=\"2999\">\n<li data-start=\"2841\" data-end=\"2999\">\n<p data-start=\"2843\" data-end=\"2999\">Ambas gr\u00e1ficas son sim\u00e9tricas respecto a la recta <strong data-start=\"2893\" data-end=\"2906\"><span class=\"katex\"><span class=\"katex-mathml\">y=xy = x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/strong>.<br data-start=\"2907\" data-end=\"2910\" \/>Esto significa que la funci\u00f3n inversa refleja el comportamiento de la funci\u00f3n original.<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"3001\" data-end=\"3004\" \/>\n<h2 data-start=\"3006\" data-end=\"3042\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f30d.svg\" alt=\"\ud83c\udf0d\" \/> Aplicaciones en la vida real<\/h2>\n<ul data-start=\"3043\" data-end=\"3309\">\n<li data-start=\"3043\" data-end=\"3116\">\n<p data-start=\"3045\" data-end=\"3116\"><strong data-start=\"3045\" data-end=\"3066\">C\u00e1lculo de tasas:<\/strong> convertir de velocidad a tiempo y viceversa. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/23f1.svg\" alt=\"\u23f1\ufe0f\" \/><\/p>\n<\/li>\n<li data-start=\"3117\" data-end=\"3182\">\n<p data-start=\"3119\" data-end=\"3182\"><strong data-start=\"3119\" data-end=\"3132\">Econom\u00eda:<\/strong> pasar de costo a precio y de precio a costo. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4b0.svg\" alt=\"\ud83d\udcb0\" \/><\/p>\n<\/li>\n<li data-start=\"3183\" data-end=\"3246\">\n<p data-start=\"3185\" data-end=\"3246\"><strong data-start=\"3185\" data-end=\"3201\">Inform\u00e1tica:<\/strong> codificaci\u00f3n y decodificaci\u00f3n de datos. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4bb.svg\" alt=\"\ud83d\udcbb\" \/><\/p>\n<\/li>\n<li data-start=\"3247\" data-end=\"3309\">\n<p data-start=\"3249\" data-end=\"3309\"><strong data-start=\"3249\" data-end=\"3260\">F\u00edsica:<\/strong> relaciones entre fuerza, energ\u00eda o trabajo. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2699.svg\" alt=\"\u2699\ufe0f\" \/><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"3311\" data-end=\"3314\" \/>\n<h2 data-start=\"3316\" data-end=\"3343\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f393.svg\" alt=\"\ud83c\udf93\" \/> Aprender con PRONEA<\/h2>\n<p data-start=\"3344\" data-end=\"3625\">El <strong data-start=\"3347\" data-end=\"3402\">Programa Nacional de Educaci\u00f3n Alternativa \u2013PRONEA\u2013<\/strong> del Ministerio de Educaci\u00f3n de Guatemala ofrece recursos accesibles para comprender conceptos como la <strong data-start=\"3505\" data-end=\"3524\">funci\u00f3n inversa<\/strong>, ayudando a j\u00f3venes y adultos a desarrollar competencias matem\u00e1ticas aplicables en la vida diaria.<\/p>\n<hr data-start=\"3627\" data-end=\"3630\" \/>\n<h2 data-start=\"3632\" data-end=\"3649\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2705.svg\" alt=\"\u2705\" \/> Conclusi\u00f3n<\/h2>\n<p data-start=\"3650\" data-end=\"3887\">La <strong data-start=\"3653\" data-end=\"3685\">funci\u00f3n inversa y su gr\u00e1fica<\/strong> nos muestran que las matem\u00e1ticas no son solo n\u00fameros, sino relaciones que se reflejan y complementan. Aprender a identificarlas y graficarlas abre nuevas formas de interpretar problemas y soluciones.<\/p>\n<p data-start=\"3889\" data-end=\"3990\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f449.svg\" alt=\"\ud83d\udc49\" \/> Con el <strong data-start=\"3899\" data-end=\"3909\">PRONEA<\/strong>, cada paso en matem\u00e1ticas es un avance en tu formaci\u00f3n personal y profesional.<\/p>\n<\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":1281,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"image","meta":{"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"footnotes":""},"categories":[33,39],"tags":[],"class_list":["post-1276","post","type-post","status-publish","format-image","has-post-thumbnail","hentry","category-matematicas","category-recursos","post_format-post-format-image"],"_links":{"self":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1276","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1276"}],"version-history":[{"count":2,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1276\/revisions"}],"predecessor-version":[{"id":1280,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1276\/revisions\/1280"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/media\/1281"}],"wp:attachment":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1276"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1276"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1276"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}