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Tags: function, algebra, functional equation, algebra unsolved



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