Question 92
Find all functions $f: \mathbb{R} \to \mathbb{R}$ such that
$$ (x + f(x)^2)f(y) = f(yf(x)) + xyf(x) $$
for all $x, y \in \mathbb{R}$.
$$ (x + f(x)^2)f(y) = f(yf(x)) + xyf(x) $$
for all $x, y \in \mathbb{R}$.
MathNet 2012 Question 92
Math Olympiad Vault · MathNet 2012