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

In this video, we review some properties of inverse functions, in preparation for our discussion of the relationship between their slopes, which will be discussed in the next video.
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.
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