Inverse Functions (Set Theory)

In this video, we introduce the notion of the inverse of a relation. We show that the inverse relation of a function is a function if and only if the function is bijective. We also introduce the identity function and an alternative notion of inverse functions using function composition. We prove these two notions of invertibility of functions are equivalent. We consider some examples.
This is lecture 33 of the lecture series offered by Dr. Andrew Misseldine for the course Math 3120 - Transition to Advanced Mathematics at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at: drive.google.c...
This lecture is based upon Section 12.5 of Book of Proof (www.people.vcu...) by Richard Hammack, from the corresponding sections of A Transition to Advanced Mathematics (math.byu.edu/~...) by Darrin Doud and Pace P. Nielsen, and from Dr. Misseldine's own notes. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.