Inverse Functions
Introduction
An inverse function is a function that undoes another function, much like addition undoes subtraction. Inverse functions use inverse operations to turn inputs into outputs and vice versa.If a function answers the question: “Alice worked this long; how much money has she made?†Then its inverse answers the question: “Alice made this much money; how long did she work?"
If a function answers the question: “How many hours of music fit on 12 CDs?†Then its inverse answers the question: “How many CDs do you need for 3 hours of music?â€
If a function is modeled by the rule, If a function answers the question: “How many hours of music fit on 12 CDs?†Then its inverse answers the question: “How many CDs do you need for 3 hours of music?â€
![inverse function 1 inverse function 1](https://claregladwinresd.glk12.org/pluginfile.php/898/mod_book/chapter/89/Families_Of_Functions/Images/inversef1.png)
![inverse2y inverse2y](https://claregladwinresd.glk12.org/pluginfile.php/898/mod_book/chapter/89/Families_Of_Functions/Images/inverse2y.png)
A common example of an inverse function is the Celsius-to-Fahrenheit conversion:
![CtoFconversion CtoFconversion](https://claregladwinresd.glk12.org/pluginfile.php/898/mod_book/chapter/89/Families_Of_Functions/Images/CtoFconversion.png)
where C is the Celsius temperature and F the Fahrenheit temperature.
Substituting the input 100°C into the first function gives an output of 212°F. Inversely, substituting the input 212°F into the second function gives an output of 100°C.