Question 3
Find all pairs of functions $f, g : \mathbb{Q} \to \mathbb{Q}$ that satisfy the identity
$$
f(x+y) = f(x)g(1) + g(y), \quad \forall x, y \in \mathbb{Q}
$$
and the equation $f(1) = 3$.
$$
f(x+y) = f(x)g(1) + g(y), \quad \forall x, y \in \mathbb{Q}
$$
and the equation $f(1) = 3$.