# Inverse function

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The **inverse function** of a function is a function that does the opposite of . A function has an inverse if and only if it is bijective. The inverse of a function is denoted by (not to be confused with the reciprocal of ).

Given any two functions, and (notice the reversal of the domain and codomain), we say that and are inverses of each other, denoted and if:

- for all
- for all

A function that is not bijective can be "made" invertible by restricting the domain to that where the function is one-to-one and then restricting the codomain to its image on the domain restriction. For instance, the function defined by is not bijective, and thus has no inverse, but restricting the domain of to the interval , we can obtain a function defined by , which is a bijective function.