Dictionary

inverse function en · NOUN

Pronunciation

• (Southern-England) audio

Meanings

1. 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.
   • Halving is the inverse function of doubling.
   • If an inverse function exists for a given function, then it is unique.
   • 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). 1995, Nicholas M. Karayanakis, Advanced System Modelling and Simulation with Block Diagram Languages, CRC Press, page 217:
   • An example of another function that has an inverse function is f(x)#61;4x#43;5. Its inverse is f#123;-1#125;(x)#61;#92;frac#123;x-5#125;#123;4#125;. 2014, Mary Jane Sterling, Trigonometry For Dummies, 2nd edition, Wiley, page 51:
   • The inverse function of an inverse function is the original function.
   • 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. 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)))

Forms

Relateds

invertible

Synonyms

anti-function (function that reverses the mapping action of a given function)

Translations (27)

sl inverzna funkcija (function that reverses the mapping action of a given function) · ja 逆関数 (function that reverses the mapping action of a given function) · ru обратная фу́нкция (function that reverses the mapping action of a given function) · la fūnctiō inversa (function that reverses the mapping action of a given function) · it funzione inversa (function that reverses the mapping action of a given function) · sv invers funktion (function that reverses the mapping action of a given function) · sk inverzná funkcia (function that reverses the mapping action of a given function) · es función inversa (function that reverses the mapping action of a given function) · de Umkehrfunktion (function that reverses the mapping action of a given function) · da invers funktion (function that reverses the mapping action of a given function) · tl baligtad na kabisa (function that reverses the mapping action of a given function) · nb invers funksjon (function that reverses the mapping action of a given function) · pl funkcja odwrotna (function that reverses the mapping action of a given function) · ca funció inversa (function that reverses the mapping action of a given function) · uk обернена функція (function that reverses the mapping action of a given function) · de inverse Funktion (function that reverses the mapping action of a given function) · pt função inversa (function that reverses the mapping action of a given function) · sh инверзна функција (function that reverses the mapping action of a given function) · hu inverz függvény (function that reverses the mapping action of a given function) · sh inverzna funkcija (function that reverses the mapping action of a given function) · fi käänteisfunktio (function that reverses the mapping action of a given function) · fr fonction réciproque (function that reverses the mapping action of a given function) · da omvendt funktion (function that reverses the mapping action of a given function) · ko 역함수 (function that reverses the mapping action of a given function) · nn invers funksjon (function that reverses the mapping action of a given function) · es función recíproca (function that reverses the mapping action of a given function) · cs inverzní funkce (function that reverses the mapping action of a given function)