inverse function

plural inverse functions

1. mathematicsFor 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.

   5 more examples

   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).

   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

   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)))

   Synonyms: anti-function