- #1

- 3

- 0

## Homework Statement

Suppose f (x) is a continuous function on [0;1], and 0 <= f(x) <= 1 for all x any [0;1].

(a)Show that f (x)= 1 - x for some number x.

(b)Prove the more general statement: Suppose g is continuous on [0,1] and g(0)= 1, g(1)= 0,then f(x)= g(x) for some number x.

## Homework Equations

Unsure

## The Attempt at a Solution

Neither makes sense to me. For the first one, isn't f(x) = x completely valid? Or a compressed sin function? Are they asking to show that 1-x is also valid, or that f(x) must be 1 - x no matter what?

For the second one, isn't a compressed cos function valid? It will be continuous on [0,1], g(0) = 1 and g(1) = 0. So why does g(x) = f(x) = 1-x only?

The question is copied word for word so tell me if I missed or misunderstood anything.