{"id":3528,"date":"2025-02-23T08:47:43","date_gmt":"2025-02-23T08:47:43","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=3528"},"modified":"2025-02-28T19:46:21","modified_gmt":"2025-02-28T19:46:21","slug":"funciones-que-cumplen-una-igualdad","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2025\/02\/23\/funciones-que-cumplen-una-igualdad\/","title":{"rendered":"Funciones que cumplen una igualdad"},"content":{"rendered":"<pre>Problema 6 del viernes de la Fase Local de la LXI Olimpiada Espa\u00f1ola de Matem\u00e1ticas (2025)\nSe dirige a una edad de: 16-17 a\u00f1os\n<\/pre>\n\n\n<p>Encuentra todas las funciones f : (0, +\u221e) \u2192 (0, +\u221e) que cumplen, para x, y &gt; 0 cualesquiera, la igualdad siguiente:<\/p>\n\n\n\n<p class=\"has-text-align-center\">f(x\u00b7f(y))) = f(x\u00b7y) + x<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"300\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2025\/02\/375.Funcion.png\" alt=\"\" class=\"wp-image-3529\" \/><\/figure>\n\n\n\n<p>Soluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2025\/02\/28\/solucion-a-funciones-que-cumplen-una-igualdad\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 6 del viernes de la Fase Local de la LXI Olimpiada Espa\u00f1ola de Matem\u00e1ticas (2025) Se dirige a una edad de: 16-17 a\u00f1os Encuentra todas las funciones f : (0, +\u221e) \u2192 (0, +\u221e) que cumplen, para x, y &gt; 0 cualesquiera, la igualdad siguiente: f(x\u00b7f(y))) = f(x\u00b7y) + x Soluci\u00f3n: Aqu\u00ed.<\/p>\n","protected":false},"author":4267,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2242021,1738,2242029,2849],"tags":[],"class_list":["post-3528","post","type-post","status-publish","format-standard","hentry","category-olimpiada-matematica-espanola","category-olimpiadas","category-ome","category-problemas"],"_links":{"self":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3528","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/users\/4267"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/comments?post=3528"}],"version-history":[{"count":2,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3528\/revisions"}],"predecessor-version":[{"id":3534,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3528\/revisions\/3534"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=3528"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=3528"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=3528"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}