Question 94
a) Prove that there exist differentiable functions $f : (0, \infty) \to (0, \infty)$, such that $f(f'(x)) = x$, for any $x \gt 0$.
b) Prove that there do not exist differentiable functions $f : \mathbb{R} \to \mathbb{R}$, such that $f(f'(x)) = x$, for any $x \in \mathbb{R}$.
b) Prove that there do not exist differentiable functions $f : \mathbb{R} \to \mathbb{R}$, such that $f(f'(x)) = x$, for any $x \in \mathbb{R}$.