Question 3
Let $f \colon \mathbb{R} \to \mathbb{R}$ 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 $x \leq 0$.
f(x+y) \leq yf(x) + f(f(x))
$$ for all real numbers $x$ and $y$. Prove that $f(x) = 0$ for all $x \leq 0$.