Tuesday, 11 March 2014

real analysis - About a function continuous on [0,1]

Let f:[0,1][0,1] be a continuous function. Given that f(0)=0, f(1)=1 and f(f(x))=x prove that f(x)=x.
I've been thinking about this one for ages, but I can't figure out even where to begin. Give me some hints, please?

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