Problem

Source: 2019 Taiwan TST Round 1, Day 3, Problem 1

Tags: function, algebra, functional equation



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