Is there a name for a function that satisfies $f(f(x)) = x$?

Question

I have tried to look up for a function class that satisfies $f(f(x)) = x$. I wonder if there is a dedicated name to that property.

Answer 1

A function $f:X \to X$ such that $f\circ f = \operatorname{id}_X$ is called an involution, or self-inverse (since such a function is its own inverse).