Nicholas R Kirchner
To the dismay of high school and college students everywhere, mathematicians use the same notation to describe a function's inverse as they do to describe a number's reciprocal. In general, if you confuse the two interpretations, a wrong answer will result. This talk will work through constructing functions for which equality does hold, and provide a series of constraints on when we might have equality. If equality holds and $f$ maps $(0,\infty)$ to $(0,\infty)$, then we need quite a lot of discontinuities.
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