Monotone Functions, Inverse Functions, Logarithm, General Power Part 4 - Continuity of the Inverse Function
Update: 2022-12-13
Description
In this episode we demonstrate that the inverse of continuous functions (i.e., the inverse mapping - not to confuse with the point wise reciprocal) is, too, continuous. For this we show that once a continuous functions maps an interval one-to-one into the reals it is necessarily also strictly monotone (either increasing or decreasing). This observation eventually helps us with the proof of our desired result.
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