# Inverse (function)

The inverse of a function may refer to a left inverse, right inverse, or a two-sided inverse. If it is unclear from context, it usually refers to a two-sided inverse.

All three of these are functions from with some relationship to :

Definition: Left inverse
Given a function , a left inverse of is a function satisfying .
Definition: Right inverse
Given a function , a right inverse of is a function satisfying .
Definition: Two-sided inverse
If is a function, then is a two-sided inverse of if and .