## A question about a proof: inverse of a contin. and monot. function is continuous

Hi. I need to prove that the inverse of a continuous and monotonic function is also continuous. So far I have shown that if we have

$f: (a,b) \rightarrow R$ then for each $y \in f((a,b))$ and $\epsilon >0$ we have that $f(a) (without loss of generality we can assume that f is increasing)

but I don't know what to do next.

Could you help me?