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# problem on fixed points

Home Forums Math Olympiad, I.S.I., C.M.I. Entrance problem on fixed points

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Let $f : R \to R$ be a polynomial function of degree 2 . We call $x_0$ to be a fixed point of $f$ , if $x_o$ is a solution of the equation $f(x)=x$ prove that if f and $f o f$ have same value of extremum then f has atleast 2 fixed points.

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