Determine all the functions $f : R \to R$ such that: $$x + f(xf(y)) = f(y) + yf(x)$$for all $x, y \in R$.
Source: 2009 Cuba 2.4
Tags: algebra, functional
Determine all the functions $f : R \to R$ such that: $$x + f(xf(y)) = f(y) + yf(x)$$for all $x, y \in R$.