Problem

A function is given by a table of values, a graph…

00:28

Problem 2 Medium Difficulty

(a) Suppose $ f $ is a one-to-one function with domain $ A $ and range $ B $. How is the inverse function $ f^{-1} $ defined? What is the domain of $ f^{-1} $? What is the range of $ f^{-1} $?
(b) If you are given a formula for $ f $, how do you find a formula for $ f^{-1} $?
(c) If you are given the graph of $ f $, how do you find the graph of $ f^{-1} $?

Answer

a) $f^{-1}(a)=b \operatorname{IF} f(b)=a$
Range of $f=$ Domain of $f^{-1}$
Domain of $f=$ Range of $f^{-1}$
b)
1) Write $y=f(x)$ .
2) Solve this equation for $x,$ in terms of $y$ (if possible).
3) Interchange $x$ and $y$ to express $f^{-1}$ as a function of $x .$ Thus, $y=f^{-1}(x)$
c)
The graph of $f^{-1}$ is obtained by reflecting the graph of $f$ about the line
$y=x$ .

Discussion

You must be signed in to discuss.

Top Calculus 3 Educators

Watch More Solved Questions in Chapter 1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Video Transcript

All right, let's define the inverse of F of X. So for every point with coordinates, a B on F the point be a is on F in verse now because we switch the coordinates the X and Y coordinates, we end up also switching the domain and range. So for F in verse, the domain will be be and the range will be a. Now let's look at how you find the formula for an inverse. So if you're given the formula for F, what you want to do is first switch or interchange X and Y in your formula interchange. The places put X where, why was put why, where x waas and then solve for Y. This will give you the inverse, and then you can also rename it as F inverse when you're done. Okay, Now, what about graphically? If you're given the graph of F, how do you find the graph of F in verse? It's going to be the reflection of F a cross. The line y equals X. So, for example, let's say your graph f waas something like this. And let's say the line y equals X was here then, when you reflect f a cross the line y equals X. You're going to get something like that and that would be f in verse.

Heather Z.

Oregon State University

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Problem

A function is given by a table of values, a graph…

Problem 2 Medium Difficulty

Answer

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 3 Educators

Lily A.

Catherine R.

Samuel H.

Michael J.

Calculus 3 Bootcamp

Vectors Intro

Vector Basics - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 3 Educators

Lily A.

Catherine R.

Samuel H.

Michael J.

Calculus 3 Bootcamp

Vectors Intro

Vector Basics - Example 1

Recommended Videos