#### Abstract

This thesis explores the behavior of solutions of the functional equation f^{-1}(x) = for x 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 . This thesis shows that although f^{-1 }and are usually different functions, they do indeed sometimes represent the same function. This thesis will also provide methods of generating solutions of the functional equation f^{-1}(x) = f for x Dom(f).

#### Graduation Date

1995

#### Semester

Summer

#### Advisor

Sherwood, Howard

#### Degree

Master of Science (M.S.)

#### College

College of Arts and Sciences

#### Department

Mathematics

#### Format

#### Pages

51 p.

#### Language

English

#### Rights

Written permission granted by copyright holder to the University of Central Florida Libraries to digitize and distribute for nonprofit, educational purposes.

#### Length of Campus-only Access

None

#### Access Status

Masters Thesis (Open Access)

#### Identifier

DP0019492

#### Subjects

Arts and Sciences -- Dissertations, Academic; Dissertations, Academic -- Arts and Sciences

#### STARS Citation

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.

http://stars.library.ucf.edu/rtd/3139