Question 117
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that
$$
(x-y)(f(x)+f(y)) \leqslant f\left(x^{2}-y^{2}\right) \quad \text{ for all } x, y \in \mathbb{R}
$$
$$
(x-y)(f(x)+f(y)) \leqslant f\left(x^{2}-y^{2}\right) \quad \text{ for all } x, y \in \mathbb{R}
$$