# Thread: continuos function

1. ## continuos function

suppose f: [a,b] ->R is increasing
and for every Y in [f(a), f(b)], there is some x0 in [a,b] such that f(x0) = Y

I want to show that f is a continious function but dont know how to go about this problem , can some one please help ..thanks

2. Originally Posted by dopi
suppose f: [a,b] ->R is increasing
and for every Y in [f(a), f(b)], there is some x0 in [a,b] such that f(x0) = Y

I want to show that f is a continious function but dont know how to go about this problem , can some one please help ..thanks
If $f(x)$ is strictly increasing and maps intervals into intervals. Then $f(x)$ must be continous.

Use the above fact to prove this partial conversve of the intermediate value theorem.