Question 187
Find all functions $f : \mathbb{R} \to \mathbb{R}$ such that
$$
2(y + 1)f(x)f(y - 1) = 2yf(xy) - f(2x)
$$
for all $x, y \in \mathbb{R}$.
$$
2(y + 1)f(x)f(y - 1) = 2yf(xy) - f(2x)
$$
for all $x, y \in \mathbb{R}$.
MathNet 2023-part-05 — 191 problems (EN–VI) Question 187
Math Olympiad Vault · MathNet 2023-part-05 — 191 problems (EN–VI)