Problem

Source: Indonesia National Math Olympiad 2022 Problem 1 (INAMO 2022/1)

Tags: functional equation, Functional equation in R, Indonesia, Indonesia MO



Determine all functions $f: \mathbb{R} \to \mathbb{R}$ such that for any $x,y \in \mathbb{R}$ we have \[ f(f(f(x)) + f(y)) = f(y) - f(x) \]