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FUNCTIONS AND THEIR INVERSES

S. Litvinov1, E. Litvinova2

1Pennsylvania State University Hazleton (UNITED STATES)
2Bloomsburg University (UNITED STATES)
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.