Question 49
Find all functions $f: \mathbb{R} \to \mathbb{R}$ such that for all $x, y \in \mathbb{R}$,
$$
x f(x + f(y)) = (y - x) f(f(x)).
$$
$$
x f(x + f(y)) = (y - x) f(f(x)).
$$
MathNet 2023-part-01 — 191 problems (EN–VI) Question 49
Math Olympiad Vault · MathNet 2023-part-01 — 191 problems (EN–VI)