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!
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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!
(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.
Quote:
Originally Posted by georgec5594
Hypothesis (iii) is irrelevant. If f is strictly monotonic then, f is injective.
