Let f: $\displaystyle \Re$ $\displaystyle \rightarrow$ $\displaystyle \Re$

be a real-valued function defined on the set of real numbers that satisfies:

$\displaystyle f(x+y) $ ≤ $\displaystyle yf(x)+f(f(x))$

for all real numbers $\displaystyle x$ and $\displaystyle y$. Prove that $\displaystyle f(x)=0$ for all $\displaystyle x$≤$\displaystyle 0$.