Problem

Source: Bundeswettbewerb Mathematik 2016, Round 2 - #3

Tags: function, Putnam, algebra, functional equation



Find all functions $f$ that is defined on all reals but $\tfrac13$ and $- \tfrac13$ and satisfies \[ f \left(\frac{x+1}{1-3x} \right) + f(x) = x \]for all $x \in \mathbb{R} \setminus \{ \pm \tfrac13 \}$.