Question 138
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ for which
$$
f\left(x^{2}\right)-f\left(y^{2}\right) \leq (f(x)+y)(x-f(y))
$$
for all $x, y \in \mathbb{R}$.
$$
f\left(x^{2}\right)-f\left(y^{2}\right) \leq (f(x)+y)(x-f(y))
$$
for all $x, y \in \mathbb{R}$.