9.0 Inverse of a Function

Let $f:A \to B$ be bijection. Then the function $g:B \to A$ which associates each element $y \in B$ to a unique element $x \in A$ such that $f(x) = y$ is called the inverse of $f$.

$$f(x) = y \Rightarrow g(y) = x$$

The inverse of $f$ is generally denoted by ${f^{ - 1}}$.