# Lesson 6 Well Versed Solidify Understanding

## Learning Focus

Find the inverse of a function given any representation.

How can we find the equation of an inverse efficiently?

Technology guidance for today’s lesson:

- Compare Inverse Linear Functions in Tables and Graphs: Casio ClassPad Casio fx-9750GIII

## Open Up the Math: Launch, Explore, Discuss

In this lesson, you will be using the characteristics of inverse functions to develop a deeper understanding of the relationship between the equations of inverse functions and a process for finding the equation of the inverse of a function. Keep an eye out for useful patterns and relationships between functions as you work the problems.

### 1.

You are given the function

Use the two representations and the relationships you learned in the previous lesson to find an equation for

. What relationship do you see between the equations of

and ?

### 2.

This time, you are given

Use the two representations and the relationships you learned in the previous lesson to find an equation for

. What relationship do you see between the equations of

and ?

### 3.

Here’s another one where

Find the equation of

. What relationship do you see between the equations of

and ?

Find the equation of the inverse function. Show that you have checked your work with the relationship:

If

### 4.

### 5.

The graph and the equation of

### 6.

Equation of

### 7.

Equation of

## Ready for More?

Find the graph and equation of

Graph of

Equation of

## Takeaways

Finding inverse functions algebraically:

## Lesson Summary

In this lesson, we learned that the equation of an inverse function will contain the inverse operations in the reverse order. We used this idea to find a procedure to solve for the equation of the inverse of a function.

### 1.

Create a piecewise function for the graph.

### 2.

Graph the piecewise function,

### 3.

Solve for