1. May 16, 2007

### jmich79

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

Suppose that f is ais continuos function defined on [0,1] with f(0)=1 and f(1)=0. show that there is a value of x that in [0,1] such that f(x)=x. Thank You.

2. May 16, 2007

### NateTG

This is slightly simpler:
Let's say I have a function $g:[0,1] \rightarrow \Re$, which is continuous, with $g(0)=1$ and $g(1)=-1$ can you show that there is an $x \in [0,1]$ so that $g(x)=0$?

3. May 16, 2007

### jmich79

Im Still Not Following. Can You Explain It A Little Bit Better To Me. Thank You For Your Post By The Way.

4. May 16, 2007

### Office_Shredder

Staff Emeritus
If a function that's continuous is negative at one point, and positive at another point, does it necesarily cross the x-axis (i.e. is zero somewhere in between)?

That's what he's driving at, but puts it in terms that are more obviously applicable to the problem at hand

5. May 16, 2007

### Dick

Define the function G(x)=f(x)-x. Now four questions. i) is G continuous? ii) What are G(0) and G(1)? iii) What does it mean if G(x)=0 in terms of f? iv) Might this have something to do with the NateTG's and Office_Shredder's hints?