Inverses Relationsand Functions Inverses of of Relations Functions

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Inverses Relationsand Functions Inverses of of Relations Functions • How do we graph and

Inverses Relationsand Functions Inverses of of Relations Functions • How do we graph and recognize inverses of relations and functions? • How do we find inverses of functions? Holt. Mc. Dougal Algebra 2 Holt

Inverses of Relations and Functions You can also find the inverse function by writing

Inverses of Relations and Functions You can also find the inverse function by writing the original function with x and y switched and then solving for y. Holt Mc. Dougal Algebra 2

Inverses of Relations and Functions Example 1: Writing and Graphing Inverse Functions 1 Graph

Inverses of Relations and Functions Example 1: Writing and Graphing Inverse Functions 1 Graph f(x) = – 2 x – 5. Then write the inverse and graph. 1 y=– 2 x – 5 Set y = f(x). 1 x=– 2 y – 5 Switch x and y. 1 x+5=– 2 y – 2 x – 10 = y y = – 2 x - 10 f– 1(x) = – 2 x – 10 Holt Mc. Dougal Algebra 2 Solve for y. f f – 1

Inverses of Relations and Functions Example 2: Writing and Graphing Inverse Functions Graph f(x)

Inverses of Relations and Functions Example 2: Writing and Graphing Inverse Functions Graph f(x) = 2 x + 2. Then write the inverse 3 and graph. Set y = f(x). Switch x and y. Solve for y. Holt Mc. Dougal Algebra 2 f f– 1

Inverses of Relations and Functions Example 3: Graphing Inverse Functions Given the graph of

Inverses of Relations and Functions Example 3: Graphing Inverse Functions Given the graph of f(x), graph f -1 (x). Find points on the graph x Reflects over the line y = x. Holt Mc. Dougal Algebra 2 y Switch x and y. x y

Inverses of Relations and Functions Example 4: Retailing Applications Juan buys a CD online

Inverses of Relations and Functions 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. 80 L + 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. Holt Mc. Dougal Algebra 2

Inverses of Relations and Functions Example 5: Retailing Applications To make tea, use 1

Inverses of Relations and Functions Example 5: Retailing Applications To make tea, use 1 teaspoon of tea per ounce of water plus a 6 teaspoon for the pot. Find the number of ounces of water needed if 7 teaspoons of tea are used. 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. Holt Mc. Dougal Algebra 2

Inverses of Relations and Functions Lesson 8. 2 Practice B Holt Mc. Dougal Algebra

Inverses of Relations and Functions Lesson 8. 2 Practice B Holt Mc. Dougal Algebra 2

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