"Let `f:[0,1] rarr [0,1]` be a continuous function. Then prove that `f(x)=x` for at least one

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Let `f : [0, 1] rarr [0, 1] `be a continuous function such that `f (f (x))=1 for all x in[0,1] Let `f : [0, 1] rarr [0, 1] `be a continuous function such that `f (f (x))=1 for all x in[0,1]
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