Question 163
Determine the functions $f : \mathbb{Q} \to \mathbb{Q}$ and $g : \mathbb{Q} \to \mathbb{Q}$ for which
$$
g(f(x+y)) = f(x) + y g(y) - a x, \forall x, y \in \mathbb{Q},
$$
where $a \in \mathbb{Q}^*$ is given.
$$
g(f(x+y)) = f(x) + y g(y) - a x, \forall x, y \in \mathbb{Q},
$$
where $a \in \mathbb{Q}^*$ is given.