I was wondering if someone could help me with a proof:

Suppose we have the functionfsuch thatfis:

(i) continuous

(ii) strictly monotonic

(iii) injective

Prove the inverse offis continuous.

Much appreciated!

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- May 3rd 2011, 09:05 PMgeorgec5594Continuity of inverse of a continuous function
I was wondering if someone could help me with a proof:

Suppose we have the function*f*such that*f*is:

(i) continuous

(ii) strictly monotonic

(iii) injective

Prove the inverse of*f*is continuous.

Much appreciated! - May 3rd 2011, 09:49 PMTinyboss
(Assuming you have already shown or aren't asked to show that f has an inverse in the first place)

It will be enough to show that f is open, that is, for any open set U, f(U) is also an open set. In fact, it suffices to consider open intervals. See where you can go from there. - May 3rd 2011, 11:28 PMFernandoRevilla