Let $f:X \to Y$ be an invertible function. Show that the inverse of ${f^{ - 1}}$is $f,$ i.e., ${({f^{ - 1}})^{ - 1}} = f.$

We know that $f:X \to Y$

As f is invertible $\Rightarrow$ f is one-one and onto $\Rightarrow$ ${f^{ - 1}}$ exists.

Also, ${f^{ - 1}}$is one-one and onto $\Rightarrow$ ${f^{ - 1}}$ is invertible.

$\Rightarrow$ ${({f^{ - 1}})^{ - 1}}$ exists $\Rightarrow$ ${({f^{ - 1}})^{ - 1}} = f$