Problem

Source: Indonesian Stage 1 TST for IMO 2022, Test 4 (Algebra)

Tags: algebra, fe, functions, inequalities



Determine all functions $f : \mathbb{R} \to \mathbb{R}$ satisfying \[ f(a^2) - f(b^2) \leq (f(a)+b)(a-f(b)) \]for all $a,b \in \mathbb{R}$.