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 methods of generating solutions of the functional equation f-1(x)= 1/f(x) for x ε Dom(f).
Master of Science (M.S.)
College of Arts and Sciences
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Masters Thesis (Open Access)
Arts and Sciences -- Dissertations, Academic; Dissertations, Academic -- Arts and Sciences
Anschuetz, Robert Rudolph, "Behavior of the Solutions to a Functional Equation Which Equates a Function's Inverse to its Reciprocal" (1995). Retrospective Theses and Dissertations. 3139.