See inverse function in All languages combined, or Wiktionary
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Karayanakis, Advanced System Modelling and Simulation with Block Diagram Languages, CRC Press, page 217:", "text": "In the context of linearization, we recall the reflective property of inverse functions; the ƒ curve contains the point (a,b) if and only if the ƒ⁻¹ curve contains the point (b,a).", "type": "quote" }, { "ref": "2014, Mary Jane Sterling, Trigonometry For Dummies, 2nd edition, Wiley, page 51:", "text": "An example of another function that has an inverse function is f(x)#x3D;4x#x2B;5.\nIts inverse is f#x7B;-1#x7D;(x)#x3D;#x5C;frac#x7B;x-5#x7D;#x7B;4#x7D;.", "type": "quote" }, { "ref": "2014, Mark Ryan, Calculus For Dummies, Wiley, 2nd Edition, page 147, If f and g are inverse functions, then f'(x)=1/(g'(f(x)))", "text": "In words, this formula says that the derivative of a function, f, with respect to x, is the reciprocal of the derivative of its inverse function with respect to f." } ], "glosses": [ "For a given function f, another function, denoted f⁻¹, that reverses the mapping action of f; (formally) given a function f:X→Y, a function g:Y→X such that, ∀x∈X,f(x)=y⟹g(y)=x." ], "id": "en-inverse_function-en-noun-~WaU1SEd", "links": [ [ "mathematics", "mathematics" ], [ "function", "function" ] ], "raw_glosses": [ "(mathematics) For a given function f, another function, denoted f⁻¹, that reverses the mapping action of f; (formally) given a function f:X→Y, a function g:Y→X such that, ∀x∈X,f(x)=y⟹g(y)=x." ], "related": [ { "word": "invertible" } ], "synonyms": [ { "raw_tags": [ "in this sense" ], "sense": "function that reverses the mapping action of a given function", "tags": [ "nonstandard", "obsolete" ], "word": "anti-function" } ], "topics": [ "mathematics", "sciences" ], "translations": [ { "code": "ca", "lang": "Catalan", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "funció inversa" }, { "code": "cs", "lang": "Czech", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "inverzní funkce" }, { "code": "da", "lang": "Danish", "sense": "function that reverses the mapping action of a given function", "tags": [ "common-gender" ], "word": "invers funktion" }, { "code": "da", "lang": "Danish", "sense": "function that reverses the mapping action of a given function", "tags": [ "common-gender" ], "word": "omvendt funktion" }, { "code": "fi", "lang": "Finnish", "sense": "function that reverses the mapping action of a given function", "word": "käänteisfunktio" }, { "code": "fr", "lang": "French", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "fonction réciproque" }, { "code": "de", "lang": "German", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "Umkehrfunktion" }, { "code": "de", "lang": "German", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "inverse Funktion" }, { "code": "hu", "lang": "Hungarian", "sense": "function that reverses the mapping action of a given function", "word": "inverz függvény" }, { "code": "it", "lang": "Italian", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "funzione inversa" }, { "code": "ja", "lang": "Japanese", "roman": "gyaku-kansū", "sense": "function that reverses the mapping action of a given function", "word": "逆関数" }, { "code": "ko", "lang": "Korean", "roman": "yeokhamsu", "sense": "function that reverses the mapping action of a given function", "word": "역함수" }, { "code": "la", "lang": "Latin", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "fūnctiō inversa" }, { "code": "nb", "lang": "Norwegian Bokmål", "sense": "function that reverses the mapping action of a given function", "tags": [ "masculine" ], "word": "invers funksjon" }, { "code": "nn", "lang": "Norwegian Nynorsk", "sense": "function that reverses the mapping action of a given function", "tags": [ "masculine" ], "word": "invers funksjon" }, { "code": "pl", "lang": "Polish", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "funkcja odwrotna" }, { "code": "pt", "lang": "Portuguese", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "função inversa" }, { "code": "ru", "lang": "Russian", "roman": "obratnaja fúnkcija", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "обратная фу́нкция" }, { "code": "sh", "lang": "Serbo-Croatian", "sense": "function that reverses the mapping action of a given function", "tags": [ "Cyrillic", "feminine" ], "word": "инверзна функција" }, { "code": "sh", "lang": "Serbo-Croatian", "sense": "function that reverses the mapping action of a given function", "tags": [ "Roman", "feminine" ], "word": "inverzna funkcija" }, { "code": "sk", "lang": "Slovak", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "inverzná funkcia" }, { "code": "sl", "lang": "Slovene", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "inverzna funkcija" }, { "code": "es", "lang": "Spanish", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "función recíproca" }, { "code": "es", "lang": "Spanish", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "función inversa" }, { "code": "sv", "lang": "Swedish", "sense": "function that reverses the mapping action of a given function", "tags": [ "common-gender" ], "word": "invers funktion" }, { "code": "tl", "lang": "Tagalog", "sense": "function that reverses the mapping action of a given function", "word": "baligtad na kabisa" }, { "code": "uk", "lang": "Ukrainian", "roman": "obernena funkcija", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "обернена функція" } ], "wikipedia": [ "inverse function" ] } ], "word": "inverse function" }
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Karayanakis, Advanced System Modelling and Simulation with Block Diagram Languages, CRC Press, page 217:", "text": "In the context of linearization, we recall the reflective property of inverse functions; the ƒ curve contains the point (a,b) if and only if the ƒ⁻¹ curve contains the point (b,a).", "type": "quote" }, { "ref": "2014, Mary Jane Sterling, Trigonometry For Dummies, 2nd edition, Wiley, page 51:", "text": "An example of another function that has an inverse function is f(x)#x3D;4x#x2B;5.\nIts inverse is f#x7B;-1#x7D;(x)#x3D;#x5C;frac#x7B;x-5#x7D;#x7B;4#x7D;.", "type": "quote" }, { "ref": "2014, Mark Ryan, Calculus For Dummies, Wiley, 2nd Edition, page 147, If f and g are inverse functions, then f'(x)=1/(g'(f(x)))", "text": "In words, this formula says that the derivative of a function, f, with respect to x, is the reciprocal of the derivative of its inverse function with respect to f." } ], "glosses": [ "For a given function f, another function, denoted f⁻¹, that reverses the mapping action of f; (formally) given a function f:X→Y, a function g:Y→X such that, ∀x∈X,f(x)=y⟹g(y)=x." ], "links": [ [ "mathematics", "mathematics" ], [ "function", "function" ] ], "raw_glosses": [ "(mathematics) For a given function f, another function, denoted f⁻¹, that reverses the mapping action of f; (formally) given a function f:X→Y, a function g:Y→X such that, ∀x∈X,f(x)=y⟹g(y)=x." ], "topics": [ "mathematics", "sciences" ], "wikipedia": [ "inverse function" ] } ], "synonyms": [ { "raw_tags": [ "in this sense" ], "sense": "function that reverses the mapping action of a given function", "tags": [ "nonstandard", "obsolete" ], "word": "anti-function" } ], "translations": [ { "code": "ca", "lang": "Catalan", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "funció inversa" }, { "code": "cs", "lang": "Czech", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "inverzní funkce" }, { "code": "da", "lang": "Danish", "sense": "function that reverses the mapping action of a given function", "tags": [ "common-gender" ], "word": "invers funktion" }, { "code": "da", "lang": "Danish", "sense": "function that reverses the mapping action of a given function", "tags": [ "common-gender" ], "word": "omvendt funktion" }, { "code": "fi", "lang": "Finnish", "sense": "function that reverses the mapping action of a given function", "word": "käänteisfunktio" }, { "code": "fr", "lang": "French", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "fonction réciproque" }, { "code": "de", "lang": "German", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "Umkehrfunktion" }, { "code": "de", "lang": "German", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "inverse Funktion" }, { "code": "hu", "lang": "Hungarian", "sense": "function that reverses the mapping action of a given function", "word": "inverz függvény" }, { "code": "it", "lang": "Italian", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "funzione inversa" }, { "code": "ja", "lang": "Japanese", "roman": "gyaku-kansū", "sense": "function that reverses the mapping action of a given function", "word": "逆関数" }, { "code": "ko", "lang": "Korean", "roman": "yeokhamsu", "sense": "function that reverses the mapping action of a given function", "word": "역함수" }, { "code": "la", "lang": "Latin", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "fūnctiō inversa" }, { "code": "nb", "lang": "Norwegian Bokmål", "sense": "function that reverses the mapping action of a given function", "tags": [ "masculine" ], "word": "invers funksjon" }, { "code": "nn", "lang": "Norwegian Nynorsk", "sense": "function that reverses the mapping action of a given function", "tags": [ "masculine" ], "word": "invers funksjon" }, { "code": "pl", "lang": "Polish", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "funkcja odwrotna" }, { "code": "pt", "lang": "Portuguese", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "função inversa" }, { "code": "ru", "lang": "Russian", "roman": "obratnaja fúnkcija", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "обратная фу́нкция" }, { "code": "sh", "lang": "Serbo-Croatian", "sense": "function that reverses the mapping action of a given function", "tags": [ "Cyrillic", "feminine" ], "word": "инверзна функција" }, { "code": "sh", "lang": "Serbo-Croatian", "sense": "function that reverses the mapping action of a given function", "tags": [ "Roman", "feminine" ], "word": "inverzna funkcija" }, { "code": "sk", "lang": "Slovak", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "inverzná funkcia" }, { "code": "sl", "lang": "Slovene", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "inverzna funkcija" }, { "code": "es", "lang": "Spanish", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "función recíproca" }, { "code": "es", "lang": "Spanish", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "función inversa" }, { "code": "sv", "lang": "Swedish", "sense": "function that reverses the mapping action of a given function", "tags": [ "common-gender" ], "word": "invers funktion" }, { "code": "tl", "lang": "Tagalog", "sense": "function that reverses the mapping action of a given function", "word": "baligtad na kabisa" }, { "code": "uk", "lang": "Ukrainian", "roman": "obernena funkcija", "sense": "function that reverses the mapping action of a given function", "tags": [ "feminine" ], "word": "обернена функція" } ], "word": "inverse function" }
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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