Question 120
Let $\alpha \neq 0$. Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that for all real numbers $x, y$,
$$
f\left(x^{2}+y+f(y)\right)=f(x)^{2}+\alpha y
$$
$$
f\left(x^{2}+y+f(y)\right)=f(x)^{2}+\alpha y
$$
MathNet 2023-part-02 — 191 problems (EN–VI) Question 120
Math Olympiad Vault · MathNet 2023-part-02 — 191 problems (EN–VI)