# Real analysis: Existence Of A Fixed Point

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Let f be a continuous function on the closed interval [0,1] with range also contained in [0,1].Prove that f must have a fixed point; that is, show f(x)=x for at least one value of x belong to [0,1].

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##### Solution Summary

The solution is comprised of a proof regarding the existence of a fixed point.

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Proof:

We consider the function g(x)=f(x)-x

From the condition, the range of f(x) ...

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