“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) = (π²)/x, where x ≠ 0, x ∈ mathbbR. Show…

Let y = f(x) ∴ y = (π²)/x ⇒ x = (π²)/y f⁻¹(x) = (π²)/x ∴ f(x) is a self-inverse function. Let y = f(x) ∴ y = (π²)/x ⇒ x = (π²)/y f⁻¹(x) = (π²)/x ∴ f(x) is a self-inverse function.

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Mathematics20252 marksDerivationRelations and Functions

Prove the following.

“A function f is called a self-inverse function if f⁻¹(x) = f(x) for all values of x in the…

“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.

Answer

Official answer key

Let $y = f(x)$ $\therefore y = \frac{\pi^2}{x} \Rightarrow x = \frac{\pi^2}{y}$ $f^{-1}(x) = \frac{\pi^2}{x}$ $\therefore f(x)$ is a self-inverse function.

Let $y = f(x)$
$\therefore y = \frac{\pi^2}{x} \Rightarrow x = \frac{\pi^2}{y}$
$f^{-1}(x) = \frac{\pi^2}{x}$
$\therefore f(x)$ is a self-inverse function.