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Today 8/23/19 Section 1.5 Inverse Functions Notes and examples In class Discussion and Assignment Homework 1
17

Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

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Page 1: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

Today 8/23/19Section 1.5 Inverse Functions

Notes and examples

In class Discussion and Assignment

Homework

1

Page 2: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

1.5 Inverse Functions

13/11/2015 2

Page 3: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

1.5 Inverse Functions

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Page 4: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

Inverse Functions

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Page 5: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

How to find the InverseWhen f(x) is given:

1) Replace f(x) with y

2) Interchange x and y

3) Solve for y This y becomes f-1(x)

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Page 6: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

Example f(x) = 2x - 18

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Page 7: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

One to One functionsHow to tell:

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Page 8: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

Example 2

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Page 9: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

Solution

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Page 10: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

Bell-work 8/23

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Page 11: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

Solution

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Page 12: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

Reflection The graph of f(x) and its inverse are reflected across the line

y = x.

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Page 13: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

Trig functions and their inverses

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Page 14: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

Domain and Range of Trig Functions

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Page 15: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

Inverse Trig Functions

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Page 16: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

Try

13/11/2015 16

Page 17: Section 1.5 Inverse Functions Notes and examples In class ...€¦ · Inverse Trig Functions 13/11/2015 15. Try 13/11/2015 16. 1.5 Assignment Pgs. 41 #1, 2, 4, 5, 17, 23-28 13/11/2015

1.5 AssignmentPgs. 41

#1, 2, 4, 5, 17, 23-28

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