In this lesson, students continue to develop their understanding of inverse functions. Previously, students wrote inverses for functions where the input and output were related by one operation. Here, they write inverses for functions that are defined using multiple operations, recognizing that the process is comparable to their earlier work of solving for a variable. Students also interpret the inverse functions in terms of situations, and in doing so practice reasoning quantitatively and abstractly (MP2).
The functions students see here and in the next lesson are limited to linear functions.
- Find the inverse of a linear function by solving an equation for the input variable.
- Interpret an inverse function in terms of the quantities in a situation.
Let’s find the inverse of linear functions.
- I can explain the meaning of an inverse function in terms of a situation.
- When I have an equation that defines a linear function, I know how to find its inverse.
Two functions are inverses to each other if their input-output pairs are reversed, so that if one functions takes \(a\) as input and gives \(b\) as an output, then the other function takes \(b\) as an input and gives \(a\) as an output.
You can sometimes find an inverse function by reversing the processes that define the first function in order to define the second function.