Is there a function $f:\mathbb{R}\to\mathbb{R}$ such that $f\circ f\circ f=Id.$, but $f\neq Id.$?
$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?