Inverse Functions

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Sharp Tutor Mon, Jan 17, 2022 09:43 PM UTC

OBJECTIVES:
1. Decide whether a function is one-to-one and, if it is, find its inverse.
2. Use the horizontal line test to determine whether a function is one-to-one.
3. Find the equation of the inverse of a function.
4. Graph f^(–1) from the graph of f.

1. Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 11.1 - 1

2. Chapter 11
Inverse, Exponential
and
Logarithmic Functions
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 11.1 - 2

3. 11.1
Inverse Functions
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 11.1 - 3

4. 11.1 Inverse Functions
Objectives
1. Decide whether a function is one-to-one and,
if it is, find its inverse.
2. Use the horizontal line test to determine
whether a function is one-to-one.
3. Find the equation of the inverse of a function.
4. Graph f –1 from the graph of f.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 11.1 - 4

5. 11.1 Inverse Functions
Functions Revisited
Domain Range Domain Range
5 1 1 3
–3 0 2 0
8 3 0
4
11 2 –1
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 11.1 - 5

6. 11.1 Inverse Functions
Functions Revisited
Domain Range
5 1
–3 0
8 3
11 2
This is a function.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 11.1 - 6

7. 11.1 Inverse Functions
Functions Revisited
Domain Range
1 3
2 0
0
4
–1
This is not a function.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 11.1 - 7

8. 11.1 Inverse Functions
One-to-One Functions
Domain Range Domain Range
5 1 3
1
–3 0 2 0
8 3 0
4
11 2 –1
is one-to-one is not one-to-one
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 11.1 - 8

9. 11.1 Inverse Functions
Relationship Between One-to-One and Inverse
.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 11.1 - 9

10. 11.1 Inverse Functions
Relationship Between One-to-One and Inverse
.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 11.1 - 10

11. 11.1 Inverse Functions
Horizontal Line Test and One-to-One Functions
.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 11.1 - 11

12. 11.1 Inverse Functions
Horizontal Line Test and One-to-One Functions
.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 11.1 - 12

13. 11.1 Inverse Functions
Finding the Equation of the Inverse of a Function
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 11.1 - 13

19. 11.1 Inverse Functions
Graphing f –1 from the Graph of f
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 11.1 - 19

20. 11.1 Inverse Functions
Graphing f –1 from the Graph of f
These pairs of
points are
mirror images
with respect to
y = x.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 11.1 - 20

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