“A function is called a self-inverse function if for all values of in the domain.” Let , where …

“A function $f$ is called a self-inverse function if $f^{-1}(x) = f(x)$ for all values of $x$ in the domain.” Let $f(x) = \frac{\pi^2}{x}$, where $x \neq 0, x \in \mathbb{R}$. Show that $f(x)$ is a self-inverse function.