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Behavior Of The Solutions To A Functional Equation Which Equates A Function's Inverse To Its Reciprocal, Robert Rudolph Anschuetz

Retrospective Theses and Dissertations

This thesis explores the behavior of solutions of the functional equation f-1(x)= 1/f(x) for x ε Dom(f), where f is a real-valued function of a real variable. It is quite common to mistake the notation f^-1, which means the inverse of f with respect to composition with the inverse of f with respect to multiplication, usually denoted by 1/f. This thesis shows that although f^-1 and 1/f are usually different function, they do indeed sometimes represent the same function. This thesis will also provide …