Abstract:

Based on a long-time experience, we shall state that finding inverses of elementary functions with restricted domains could be a rather challenging task for the majority of algebra/pre-calculus/calculus students and quite often even for experienced instructors involved in teaching such courses.

This phenomenon can be easily explained: one has to be careful with the domains and ranges of the functions involved. This presentation addresses the issues that arise in the course of solving such problems for a wide variety of functions, including quadratic, irrational, exponential, logarithmic, and some polynomial and rational functions. First, we examine examples where one needs to verify whether a given function is one-to-one and if not to decide how to restrict its domain to end up with a one-to-one function. Then we outline rigorous procedures that can be employed when finding the inverses of one-to-one functions.