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Just like an old Putnam FE...

Source: Bundeswettbewerb Mathematik 2016, Round 2 - #3

September 7, 2016

functionPutnamalgebrafunctional equation

Problem Statement

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 \}