Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan...

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Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-1 Chapter 6 Section 2

Transcript of Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan...

Page 1: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-1

Chapter 6

Section 2

Page 2: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-2

Page 3: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-3

Determine Whether a

Function Is

One-to-One

Page 4: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-4

Figure

Page 5: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-5

Figure

Page 6: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-6

Definition

Page 7: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-7

Figure

Page 8: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-8

Example

Page 9: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-9

Solution

Page 10: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-10

Theorem

Page 11: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-11

Figure

Page 12: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-12

Example

Page 13: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-13

Solution

Figure 10

Page 14: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-14

Theorem

Page 15: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-15

Determine the Inverse of a Function

Defined by a Map or a Set of Ordered

Pairs

Page 16: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-16

Definition

Page 17: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-17

Example

Page 18: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-18

Solution

Page 19: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-19

Figure

Page 20: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-20

Page 21: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-21

Figure

Page 22: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-22

Example

Page 23: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-23

Solution

Page 24: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-24

Obtain the Graph of

the Inverse Function

from the Graph of

the Function

Page 25: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-25

Figure

Page 26: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-26

Theorem

Page 27: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-27

Figure

Page 28: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-28

Example

Page 29: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-29

Solution

Figure 15

Page 30: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-30

Find the Inverse of a

Function Defined by

an Equation

Page 31: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-31

Figure

Page 32: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-32

Page 33: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-33

Example

Page 34: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-34

Solution

Page 35: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-35

Solution continued

Page 36: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-36

Example

Page 37: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-37

Solution

Page 38: Algebra & Trigonometry 10th editionTitle: Algebra & Trigonometry 10th edition Author: Sullivan Subject: Section 6.2 One-to-One Functions; Inverse Functions Created Date: 10/27/2015

Copyright © 2016, 2012 Pearson Education, Inc. Chapter 6.2-38

Figure 17