2.13.1* Inverse Functions, Precalculus Review - Analytic Geometry and Calculus I

In this video, we review some properties of inverse functions that we learned in Precalculus.
Properties of inverse functions:
*Inverse functions undo each other.
*f of f inverse of x equals x and vice versa.
*The domain of f is the range of f inverse, and the range of f is the domain of f inverse.
*We can find f inverse by switching the role of x and y and solving for y.
*If (a, b) is on the graph of f, (b, a) is on the graph of f inverse. As a result, the graph of f inverse is a reflection of the graph of f across the line y=x.
*We can visually determine whether a function has an inverse using the horizontal line test. If a function passes the horizontal line test, the function is called one-to-one. That is, every x has only one y and every y has only one x.
*We can often find an inverse for a function that isn't invertible by restricting the range to an appropriate interval. We do this to y=x^2 to get the square root of x, and we do that to all six trig functions to define the six inverse trigonometric functions.
Graph on Desmos.com: www.desmos.com...
(There is an earlier version of this video on this playlist. Both have strengths and weaknesses, so both are shown here. I do a better job with the Desmos part in the original video, and a better job with the hand-written part in this video, in my opinion.)

[@SashaTownsendTulsa]

I remade this video, after watching the original version. I wanted to do the discussion with the hand-written work a little bit better than I did last time. I noticed though, after watching both videos, that the end of the original video, using the Desmos graphs, was actually pretty good. I recommend watching this one, and the end of the original, which is video #40 on the current playlist. Please let me know if you have any questions!