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€
then the inverse function is modeled by 
. Since multiplication and division are inverse operations, they will create inverse functions.A common example of an inverse function is the Celsius-to-Fahrenheit conversion:
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.