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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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shantanu deodhar
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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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shantanu deodhar
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