http://www.ck12.org Chapter 1. Functions and Graphs
1.12 Inverses of Functions
Here you will learn about inverse functions and what they look like graphically and numerically. You will also learn
how to find and verify inverse functions algebraically.
Functions are commonly known as rules that take inputs and produce outputs. An inverse function does exactly the
reverse, undoing what the original function does. How can you tell if two functions are inverses?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/57953http://www.youtube.com/watch?v=qgezKpQYH2w James Sousa: Inverse Functions
Guidance
A function is written asf(x)and its inverse is written asf−^1 (x). A common misconception is to see the -1 and
interpret it as an exponent and writef(^1 x), but this is not correct. Instead,f−^1 (x)should be viewed as a new function
from the range off(x)back to the domain.
It is important to see the cycle that starts withx, becomesyand then goes back tox. In order for two functions to
truly be inverses of each other, this cycle must hold algebraically.
f(f−^1 (x)) =xandf−^1 (f(x)) =x