Question 43
Does there exist a pair $(g, h)$ of functions $g, h : \mathbb{R} \to \mathbb{R}$ such that the only function $f : \mathbb{R} \to \mathbb{R}$ satisfying $f(g(x)) = g(f(x))$ and $f(h(x)) = h(f(x))$ for all $x \in \mathbb{R}$ is the identity function $f(x) = x$?
(This problem was suggested by Alexander Betts from the United Kingdom.)
(This problem was suggested by Alexander Betts from the United Kingdom.)