Problem

A function is self-inverse when applying it twice returns you to where you started—that is, $f(f(x)) = x$. The key insight is that reciprocals have a special symmetry: taking the reciprocal of a reciprocal undoes itself. You'll compute $f(f(x))$ by substituting $f(x)$ back into the original function and simplify to confirm you get $x$ back.

A function is self-inverse when applying it twice returns you to where you started—that is, $f(f(x)) = x$. The key insight is that reciprocals have a special symmetry: taking the reciprocal of a reciprocal undoes itself. You'll compute $f(f(x))$ by substituting $f(x)$ back into the original function and simplify to confirm you get $x$ back.