See inverse function in All languages combined, or Wiktionary
Download JSON data for inverse function meaning in English (7.9kB)
{
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{
"text": "Halving is the inverse function of doubling.",
"type": "example"
},
{
"text": "If an inverse function exists for a given function, then it is unique.",
"type": "example"
},
{
"text": "The inverse function of an inverse function is the original function.",
"type": "example"
},
{
"ref": "1995, Nicholas M. 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": "quotation"
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{
"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;.",
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"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."
}
],
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"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."
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"(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."
],
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{
"code": "ca",
"lang": "Catalan",
"sense": "function that reverses the mapping action of a given function",
"tags": [
"feminine"
],
"word": "funció inversa"
},
{
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"sense": "function that reverses the mapping action of a given function",
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{
"code": "da",
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"tags": [
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{
"code": "da",
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"sense": "function that reverses the mapping action of a given function",
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},
{
"code": "fr",
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"sense": "function that reverses the mapping action of a given function",
"tags": [
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"word": "fonction réciproque"
},
{
"code": "de",
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"tags": [
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{
"code": "de",
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"sense": "function that reverses the mapping action of a given function",
"tags": [
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"word": "inverse Funktion"
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{
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"sense": "function that reverses the mapping action of a given function",
"word": "inverz függvény"
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"sense": "function that reverses the mapping action of a given function",
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"sense": "function that reverses the mapping action of a given function",
"word": "逆関数"
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"roman": "yeokhamsu",
"sense": "function that reverses the mapping action of a given function",
"word": "역함수"
},
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{
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{
"code": "pl",
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"sense": "function that reverses the mapping action of a given function",
"tags": [
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"word": "funkcja odwrotna"
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{
"code": "pt",
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"sense": "function that reverses the mapping action of a given function",
"tags": [
"feminine"
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"word": "função inversa"
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"code": "ru",
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"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"
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"word": "инверзна функција"
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{
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"code": "es",
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"feminine"
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{
"code": "es",
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"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"
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"word": "обернена функція"
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"text": "Halving is the inverse function of doubling.",
"type": "example"
},
{
"text": "If an inverse function exists for a given function, then it is unique.",
"type": "example"
},
{
"text": "The inverse function of an inverse function is the original function.",
"type": "example"
},
{
"ref": "1995, Nicholas M. 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": "quotation"
},
{
"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;.",
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"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."
}
],
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"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."
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"(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."
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"translations": [
{
"code": "ca",
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"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"
],
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{
"code": "da",
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"sense": "function that reverses the mapping action of a given function",
"tags": [
"common-gender"
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"word": "invers funktion"
},
{
"code": "da",
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"sense": "function that reverses the mapping action of a given function",
"tags": [
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"word": "omvendt funktion"
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"lang": "Finnish",
"sense": "function that reverses the mapping action of a given function",
"word": "käänteisfunktio"
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{
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"lang": "French",
"sense": "function that reverses the mapping action of a given function",
"tags": [
"feminine"
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{
"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"
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"word": "inverzna funkcija"
},
{
"code": "sk",
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"sense": "function that reverses the mapping action of a given function",
"tags": [
"feminine"
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"word": "inverzná funkcia"
},
{
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"sense": "function that reverses the mapping action of a given function",
"tags": [
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"word": "inverzna funkcija"
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{
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"sense": "function that reverses the mapping action of a given function",
"tags": [
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"word": "función recíproca"
},
{
"code": "es",
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"sense": "function that reverses the mapping action of a given function",
"tags": [
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"word": "función inversa"
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{
"code": "sv",
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"sense": "function that reverses the mapping action of a given function",
"tags": [
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],
"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"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-04-30 from the enwiktionary dump dated 2024-04-21 using wiktextract (210104c and c9440ce). 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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