Problem

Source: USAJMO 2024/5

Tags: USA(J)MO, USAJMO, function, functional equation, PointWise Trap



Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ that satisfy \[ f(x^2-y)+2yf(x)=f(f(x))+f(y) \]for all $x,y\in\mathbb{R}$. Proposed by Carl Schildkraut