Question 160
Determine all functions $f: \mathbb{R} \to \mathbb{R}$ such that
$$
f(x + f(y)) = f(f(y)) + 2x f(y) + x^2
$$
holds for all real numbers $x$ and $y$.
$$
f(x + f(y)) = f(f(y)) + 2x f(y) + x^2
$$
holds for all real numbers $x$ and $y$.
MathNet 2017-part-01 — 176 problems (EN–VI) Question 160
Math Olympiad Vault · MathNet 2017-part-01 — 176 problems (EN–VI)