Question 21
Find all functions $f, g : \mathbb{Q} \to \mathbb{Q}$ such that, for all $x, y \in \mathbb{Q}$,
$$
f(g(x) + g(y)) = f(g(x)) + y,
$$
$$
g(f(x) + f(y)) = g(f(x)) + y,
$$
$$
f(g(x) + g(y)) = f(g(x)) + y,
$$
$$
g(f(x) + f(y)) = g(f(x)) + y,
$$