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## Homework Statement

True or False. If f(x) is continuous and 0≤ f(x) ≤ 1 for all x in the interval [0,1] then for some number, x, f(x)= x. Explain your answer.

## Homework Equations

## The Attempt at a Solution

False. I think that even though 0 and 1 are included in the domain, it is possible for the x and y values NOT to coincide.

(I googled zig zag function, because I didn't know the name, and I found the 'Weierstrass' function. I thought this would be an acceptable counterexample?)

Thank you.