Question 71
Find all functions $f: \mathbf{R} \to \mathbf{R}$ satisfying, for all real numbers $x$ and $y$, the equation
$$
|x|f(y) + yf(x) = f(xy) + f(x^2) + f(f(y)).
$$
$$
|x|f(y) + yf(x) = f(xy) + f(x^2) + f(f(y)).
$$
MathNet 2015-part-01 — 191 problems (EN–VI) Question 71
Math Olympiad Vault · MathNet 2015-part-01 — 191 problems (EN–VI)