Trigonometry Workbook For Dummies
Book image
Explore Book Buy On Amazon

You can tell that two functions are inverse functions when each one undoes what the other does. When you graph inverse functions, each is a mirror image of the other. Here are some examples of inverse functions:

image0.png

You can write all of this in one step as:

image1.png

If you write this in one step, you get:

image2.png

Don’t confuse the superscript –1 in a function with exponent –1.

image3.png

When you graph inverse functions, each is the mirror image of the other, reflected over the line
y = x.

image4.png

These functions are graphed below:

image5.jpg

If you rotate the graph in the figure counterclockwise so that the line y = x is vertical, you can easily see that these functions are mirror images of each other. One consequence of this symmetry is that if a point like (2, 4) is on one of the functions, then the point (4, 2) will be on the other.

image6.png

About This Article

This article is from the book:

About the book author:

Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

This article can be found in the category: