- #1

LilTaru

- 81

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## Homework Statement

a) Suppose that f(x) is a continuous function on [0, 1] and 0 <= f(x) <= 1 for all x in [0, 1]. Show that there is an x in [0, 1] where f(x) = x.

b) Suppose that f(x) is a continuous function on [0, 2] with f(0) = f(2). Show that there is an x in [0, 1] such that f(x) = f(x + 1).

## Homework Equations

## The Attempt at a Solution

I assume I have to use the Intermediate Value Theorem, but I have no idea how to use it! For (a) I thought 0 <= f(x) <= 1 means since f(x) is between f(a) and f(b) then there exists a c or x in this question so that f(x) = x, but I have no idea! And for (b)... not a clue! Please help?!