Question 13
Let $f, g$ be functions $\mathbb{R} \to \mathbb{R}$ such that
$$
f(g(x) + y) = g(x + y) \quad \forall x, y \in \mathbb{R}
$$
then either $f$ is the identity¹ function or $g$ is periodic².
$$
f(g(x) + y) = g(x + y) \quad \forall x, y \in \mathbb{R}
$$
then either $f$ is the identity¹ function or $g$ is periodic².