Question 7
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
$$
f(x f(x+y))=f(y f(x))+x^{2}
$$
$$
f(x f(x+y))=f(y f(x))+x^{2}
$$
IMO 2009 — Complete Shortlist Question 7
IMO Shortlist · IMO 2009 — Complete Shortlist