{"id":539980,"date":"2023-04-23T01:35:13","date_gmt":"2023-04-22T20:05:13","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/if-fgxx-and-gfxx-then-gx-is-the-inverse-of-fx%e2%8b%85g%e2%80%b2xf%e2%80%b2x1%e2%87%92g%e2%80%b2fx1f%e2%80%b2x-2\/"},"modified":"2025-06-20T13:28:19","modified_gmt":"2025-06-20T07:58:19","slug":"if-fgxx-and-gfxx-then-gx-is-the-inverse-of-fx%e2%8b%85g%e2%80%b2xf%e2%80%b2x1%e2%87%92g%e2%80%b2fx1f%e2%80%b2x-2","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/iffgxxandgfxxthengxis-the-inverse-offx\/","title":{"rendered":"If\u00a0f(g(x))=x\u00a0and\u00a0g(f(x))=x\u00a0then\u00a0g(x)\u00a0is the inverse of\u00a0f(x)\u22c5g\u2032(x)f\u2032(x)=1\u21d2g\u2032(f(x))=1f\u2032(x)"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"If\u00a0f(g(x))=x\u00a0and\u00a0g(f(x))=x\u00a0then\u00a0g(x)\u00a0is the inverse of\u00a0f(x)\u22c5g\u2032(x)f\u2032(x)=1\u21d2g\u2032(f(x))=1f\u2032(x)","custom_permalink":"question\/mathematics\/iffgxxandgfxxthengxis-the-inverse-offx\/"},"categories":[],"acf":{"question":"<p>If&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mo>(<\/mo><mi>g<\/mi><mo>(<\/mo><mi>x<\/mi><mo>)<\/mo><mo>)<\/mo><mo>=<\/mo><mi>x<\/mi><\/math>&nbsp;and&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>g<\/mi><mo>(<\/mo><mi>f<\/mi><mo>(<\/mo><mi>x<\/mi><mo>)<\/mo><mo>)<\/mo><mo>=<\/mo><mi>x<\/mi><\/math>&nbsp;then&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>g<\/mi><mo>(<\/mo><mi>x<\/mi><mo>)<\/mo><\/math>&nbsp;is the inverse of&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mo>(<\/mo><mi>x<\/mi><mo>)<\/mo><mo>\u22c5<\/mo><mfenced separators=\"|\"><mrow><msup><mi>g<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mo>(<\/mo><mi>x<\/mi><mo>)<\/mo><\/mrow><\/mfenced><msup><mi>f<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mo>(<\/mo><mi>x<\/mi><mo>)<\/mo><mo>=<\/mo><mn>1<\/mn><mo stretchy=\"false\">\u21d2<\/mo><msup><mi>g<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mo>(<\/mo><mi>f<\/mi><mo>(<\/mo><mi>x<\/mi><mo>)<\/mo><mo>)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><msup><mi>f<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mo>(<\/mo><mi>x<\/mi><mo>)<\/mo><\/mrow><\/mfrac><\/math><\/p>","options":null,"solution":"<p>If \\( f(g(x)) = x \\) and \\( g(f(x)) = x \\), then \\( g(x) \\) is the inverse of \\( f(x) \\). Given \\( g'(x) f'(x) = 1 \\), it follows that \\( g'(f(x)) = \\frac{1}{f'(x)} \\).<\/p>","subject":"Mathematics"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>If\u00a0f(g(x))=x\u00a0and\u00a0g(f(x))=x\u00a0then\u00a0g(x)\u00a0is the inverse of\u00a0f(x)\u22c5g\u2032(x)f\u2032(x)=1\u21d2g\u2032(f(x))=1f\u2032(x) - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"If\u00a0f(g(x))=x\u00a0and\u00a0g(f(x))=x\u00a0then\u00a0g(x)\u00a0is the inverse of\u00a0f(x)\u22c5g\u2032(x)f\u2032(x)=1\u21d2g\u2032(f(x))=1f\u2032(x)\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/iffgxxandgfxxthengxis-the-inverse-offx\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If\u00a0f(g(x))=x\u00a0and\u00a0g(f(x))=x\u00a0then\u00a0g(x)\u00a0is the inverse of\u00a0f(x)\u22c5g\u2032(x)f\u2032(x)=1\u21d2g\u2032(f(x))=1f\u2032(x) - 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Infinity Learn by Sri Chaitanya","description":"If\u00a0f(g(x))=x\u00a0and\u00a0g(f(x))=x\u00a0then\u00a0g(x)\u00a0is the inverse of\u00a0f(x)\u22c5g\u2032(x)f\u2032(x)=1\u21d2g\u2032(f(x))=1f\u2032(x)","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/iffgxxandgfxxthengxis-the-inverse-offx\/","og_locale":"en_US","og_type":"article","og_title":"If\u00a0f(g(x))=x\u00a0and\u00a0g(f(x))=x\u00a0then\u00a0g(x)\u00a0is the inverse of\u00a0f(x)\u22c5g\u2032(x)f\u2032(x)=1\u21d2g\u2032(f(x))=1f\u2032(x) - Infinity Learn by Sri Chaitanya","og_description":"If\u00a0f(g(x))=x\u00a0and\u00a0g(f(x))=x\u00a0then\u00a0g(x)\u00a0is the inverse of\u00a0f(x)\u22c5g\u2032(x)f\u2032(x)=1\u21d2g\u2032(f(x))=1f\u2032(x)","og_url":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/iffgxxandgfxxthengxis-the-inverse-offx\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_modified_time":"2025-06-20T07:58:19+00:00","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_site":"@InfinityLearn_","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/iffgxxandgfxxthengxis-the-inverse-offx\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/iffgxxandgfxxthengxis-the-inverse-offx\/","name":"If\u00a0f(g(x))=x\u00a0and\u00a0g(f(x))=x\u00a0then\u00a0g(x)\u00a0is the inverse of\u00a0f(x)\u22c5g\u2032(x)f\u2032(x)=1\u21d2g\u2032(f(x))=1f\u2032(x) - 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