# Homework Help: Applications with continuity

1. Sep 30, 2012

### mtayab1994

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

Let f be q function defined from [a,b] to [a,b] such that for every (x,t) in [a,b]^2:

l f(x)-f(t) l < l x-t l

1- prove that f is continuous on [a;b]

2-prove that f accepts a steadfast point in [a,b]

3. The attempt at a solution
Should i try to use the definition of a limit to show that f is continuous?
If not can someone give me headers. Thank you very much

Last edited: Sep 30, 2012
2. Sep 30, 2012

### jbunniii

Yes, for part 1, use the definition of continuity.

For part 2, I assume "accepts a steadfast point" means "has a fixed point." If so, consider the function defined by f(x) - x.