inverse function

A function is invertible when its converse relation is also a function. Such a relation is the unique inverse function.

Formally,
a function $f : X \to Y$ has inverse $f^{- 1} : Y \to X$ such that $y = f (x)$ if and only if $x = f^{- 1} (y)$ .

A function $f$ is invertible if and only if it is a bijection.

The composition of a function with its inverse is the identity map:

(f^{- 1} \circ f) (x) = (f \circ f^{- 1}) (x) = x