# IMO 2011 (Problem 3)

Let $f:\mathbb{R}\to \mathbb{R}$ be a real-valued function defined on the set of real numbers that satisfies
$f (x + y) \leq yf (x) + f (f (x))$
for all real numbers $x$ and $y$. Prove that $f(x)=0$ for all $x\leq 0$.