Question 35
Let $\alpha$ be a nonzero real number.
Determine all functions $f: \mathbb{R} \to \mathbb{R}$ with
$$
f(f(x + y)) = f(x + y) + f(x)f(y) + \alpha xy
$$
for all $x, y \in \mathbb{R}$.
Determine all functions $f: \mathbb{R} \to \mathbb{R}$ with
$$
f(f(x + y)) = f(x + y) + f(x)f(y) + \alpha xy
$$
for all $x, y \in \mathbb{R}$.