Problem

Source: 2018 Taiwan TST Round 1

Tags: function, algebra



Find all functions $ f: \mathbb{R} \to \mathbb{R} $ such that $$ f\left(f\left(x\right)+y\right) = f\left(x^2-y\right)+4\left(y-2\right)\left(f\left(x\right)+2\right) $$holds for all $ x, y \in \mathbb{R} $