# Applications with continuity

## Homework Statement

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]

## 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:

jbunniii