Question 15
Let $\alpha$ and $\beta$ be real numbers with $\beta \neq 0$. Determine all functions $f: \mathbb{R} \to \mathbb{R}$ such that
$$
f(\alpha f(x) + f(y)) = \beta x + f(y)
$$
holds for all real $x$ and $y$.
$$
f(\alpha f(x) + f(y)) = \beta x + f(y)
$$
holds for all real $x$ and $y$.