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Part of 2010 Philippine MO

Problems(1)

2010 Philippines MO P3

Source:

11/16/2015
Let R∗\mathbb{R}^* be the set of all real numbers, except 11. Find all functions f:R∗→Rf:\mathbb{R}^* \rightarrow \mathbb{R} that satisfy the functional equation x+f(x)+2f(x+2009x−1)=2010x+f(x)+2f\left(\frac{x+2009}{x-1}\right)=2010.
functionalgebrafunctional equationPMO2010