1. Inverses of Relations and Functions
Essential Questions
How do we graph and recognize inverses of relations and functions?
How do we find inverses of functions?
Holt McDougal Algebra 2
Holt Algebra 2

2. You can also find the inverse function by writing the original function with x and y switched and then solving for y.

3. Example 1: Writing and Graphing Inverse Functions
Graph f(x) = – x – 5. Then write the inverse and graph. 1 2 1 2
y = – x – 5
Set y = f(x).
f –1 1 2
x = – y – 5
Switch x and y. f
x + 5 = – y 1 2
Solve for y.
–2x – 10 = y
y = –2x - 10
f–1(x) = –2x – 10

4. Example 2: Writing and Graphing Inverse Functions
Graph f(x) = x + 2. Then write the inverse and graph. 2 3
Set y = f(x).
f–1 f
Switch x and y.
Solve for y.

5. Example 3: Graphing Inverse Functions
Given the graph of f(x), graph f -1(x).
Find points on the graph x y x y
Switch x and y.
Reflects over the line y = x.

6. Example 4: Retailing Applications
Juan buys a CD online for 20% off the list price. He has to pay $2.50 for shipping. The total charge is $ What is the list price of the CD?
Step 1 Write an equation for the total charge as a function of the list price.
c = 0.80L
Charge c is a function of list price L.
Substitute in $13.70 for c.
Solve for L.
The list price of the CD is $14.

7. Example 5: Retailing Applications
To make tea, use teaspoon of tea per ounce of water plus a teaspoon for the pot. Find the number of ounces of water needed if 7 teaspoons of tea are used. 1 6
Step 1 Write an equation for the number of ounces of water needed.
Tea t is a function of ounces of water needed z.
Substitute in 7 for t.
Solve for z.
36 ounces of water should be added.

8. Lesson 8.2 Practice B