This is my first analysis class and I'm really confused. My attempt may not make much sense because I just followed an example in my book, so any help would be greatly appreciated. Thanks!(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Suppose that f: R -> R is continuous and that its image f(R) is bounded. Prove that there is a solution of the equation f(x) = x, x in R.

2. Relevant equations

Intermediate Value Theorem.

3. The attempt at a solution

Assume there is a solution to the function f. Observe that f(-1)<0 and f(1)>0. Since f is a continuous function, by applying the Intermediate Value Theorem to the restriction f:[-1,1] -> R, we can conclude that the point x0 in the open interval (-1,1) is a solution of the function f.

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# Homework Help: Proof that there is a solution to f(x)=x

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