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## Homework Statement

Let f : [0; 1] -> [0; 1] be continuous on [0; 1]. Prove that there exists C [tex]\epsilon [0; 1][/tex] such

that f(c) = c.

## Homework Equations

## The Attempt at a Solution

I've manage to prove this by having an extra cont. function g(x)=f(x)-x .. But I am looking for easier proof