inverse function

Definitions

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.

Equivalents

8 more languages

Danskinvers funktionomvendt funktion

Suomikäänteisfunktio

Italianofunzione inversa

日本語逆関数

한국어거꿀함수역함수

Polskifunkcja odwrotna

Portuguêsfunção inversa

Русскийобратная фу́нкция

Examples

“Halving is the inverse function of doubling.”

“If an inverse function exists for a given function, then it is unique.”

“The inverse function of an inverse function is the original function.”

“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).”

“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;.”

“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.”

CEFR level