 The graph of a function f is shown. Graph the inverse and describe the relationship between the function & its inverse. xy Make a table of points from the figure. Switch the x and y coordinates. xy

xy Graph the new set of points. The graph of the inverse f is a reflection of the graph of f across the line y = x.

 Graph the function & its inverse in parametric mode.

A. Find g(x), the inverse of This can be checked quickly by graphing the original and the inverse on the Y = screen. This does not need parametric mode.

B. Find g(x), the inverse of To enter higher roots on the calculator, enter the root value first, then press MATH  5: x √

 Find the inverse of

 A function is considered one-to-one if its inverse is also a function.  Use the horizontal line test to determine if the graph of the inverse will also be a function.  If the inverse is a function it is notated f -1. **This does not mean f to the -1 power.**

 Graph each function below and determine whether it is one-to-one. A. B. C. Yes No

 Find an interval on which the function is one-to-one, and find f -1 on that interval. The function is one-to-one from [0, ∞). Using this domain the inverse would be the positive square root of x. Alternatively, if ( − ∞, 0] is chosen, negative square root of x is the inverse.

 A one-to-one function and its inverse have these properties.  Also, any two functions having both properties are one-to-one and inverses of each other. For every x in the domain of f and f -1

 Verify that f and g are inverses of each other. Since the both compositions of the functions equal x, then the functions are inverses of each other.