Question 6
Let $f$ be a function from the set of real numbers to itself that satisfies
$$
f(x+y) \leq y f(x)+f(f(x))
$$
for all real numbers $x$ and $y$. Prove that $f(x)=0$ for all $x \leq 0$.
$$
f(x+y) \leq y f(x)+f(f(x))
$$
for all real numbers $x$ and $y$. Prove that $f(x)=0$ for all $x \leq 0$.