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Find f(2) and f(1)

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December 31, 2011
functionalgebrafunctional equationalgebra unsolved

Problem Statement

Suppose f:R⟶Rf : \mathbb{R} \longrightarrow \mathbb{R} be a function such that 2f(f(x))=(x2−x)f(x)+4−2x2f (f (x)) = (x^2 - x)f (x) + 4 - 2x for all real xx. Find f(2)f (2) and all possible values of f(1)f (1). For each value of f(1)f (1), construct a function achieving it and satisfying the given equation.
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