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

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

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.