Table of Contents |
An inverse function undoes the operations performed on variables of a function.
EXAMPLE
If a number is multiplied by 2, and added by 3, we can write this as the function . The inverse to this function first subtracts 3 from the input value, and then divides by 2, so as to completely undo all operations of the original function. We write this as the inverse function .On a graph, the x- and y-coordinates between a function and its inverse are inverted or swapped. This means that for any coordinate, (x, y), of a function, we can find a corresponding coordinate on the graph of its inverse using the coordinates (y, x). This means we locate the x-value on the y-axis, and locate the y-value on the x-axis.
EXAMPLE
Check out the graph of a function and its inverse.Points on | Points on |
---|---|
(2, 7) | (7, 2) |
(-2, -1) | (-1, -2) |
If we want to find the inverse of a function algebraically, there are two common procedures most people use:
EXAMPLE
Find the inverse of using the first method where we swap x and y.Rewrite the function as | |
Swap x and y | |
Square both sides | |
Add 4 to both sides | |
Divide both sides by 2 | |
Our solution for y | |
Our solution in inverse notation |
EXAMPLE
Find the inverse of .Rewrite the function as | |
Swap x and y | |
Multiply both sides by 3 | |
Subtract 7 from both sides | |
Our solution for y | |
Our solution in inverse notation |
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT www.wallace.ccfaculty.org/book/book.html. License: Creative Commons Attribution 3.0 Unported License