Question 20
Find all functions $f$ from the set of real numbers into the set of real numbers which satisfy for all real $x, y$ the identity
$$
f(x f(x+y))=f(y f(x))+x^{2} .
$$
$$
f(x f(x+y))=f(y f(x))+x^{2} .
$$
MathNet 2009-part-02 — 175 problems (EN–VI) Question 20
Math Olympiad Vault · MathNet 2009-part-02 — 175 problems (EN–VI)