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

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

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

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.

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.

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 $13.70. 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 + 2.50 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.

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.

Lesson 8.2 Practice B