Question 13
Determine all functions $f: \mathbb{R} \to \mathbb{R}$ such that
$$
f(xf(y)) = (1-y)f(xy) + x^2y^2f(y)
$$
holds for all real numbers $x$ and $y$.
$$
f(xf(y)) = (1-y)f(xy) + x^2y^2f(y)
$$
holds for all real numbers $x$ and $y$.
MathNet 2018-part-02 — 181 problems (EN–VI) Question 13
Math Olympiad Vault · MathNet 2018-part-02 — 181 problems (EN–VI)