Question 56
Find all functions $f : \mathbb{R} \to \mathbb{R}$ such that
$$
f(a^2) - f(b^2) \leq (f(a) + b)(a - f(b)), \quad \text{for all } a, b \in \mathbb{R}.
$$
$$
f(a^2) - f(b^2) \leq (f(a) + b)(a - f(b)), \quad \text{for all } a, b \in \mathbb{R}.
$$