Problem

(a) If we shift a curve to the left, what happens…

04:08

Problem 76 Hard Difficulty

(a) Graph the function $ f(x) = \sin (\sin^{-1} x) $ and explain the appearance of the graph.
(b) Graph the function $ g(x) = \sin^{-1} (\sin x) $. How do you explain the appearance of this graph?

Answer

See explanations

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

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

graphed the function f of X equals sign of arc sine of X and explain the appearance of the graph. So for this question here, notice that this function f simplifies the X, and we all know what you know. X looks like it's, you know, it's a line through the origin with slope one. Okay, but notice that there is going to be a restriction in the domain of ass. Okay, so I suppose I noticed that the domain of the outside function sign for ex belongs to the real numbers. But the inside function, the arc sine of acts there is a restriction in the domain in X belongs from You could have wonder one. I do have this function graft here. Okay? And it's going to take a look at it. And when you have the function, why equals the art? The sign of the arc sine of X, and that does reduce down to X with domain. Ah, in which explosions from negative or from positive one. Ah, negative one. Okay, so we have the same function. Why equals X with the restriction in the domain? Okay, stick a look. A ah, the other one g equals the arc sine the sign of ax. Okay, so and notice we do have, uh, these characters six year in in their respective domains. Okay, let's go in and take a look at this graph here. So we have the ark sign. Signed X. Okay, so we look. Looks like we have these concentric, uh, you know, X negative axe. I'm going to guess this is negative X here. Okay, X in a rex. Thanks for watching.

Jeffrey P.

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) If we shift a curve to the left, what happens…

Problem 76 Hard Difficulty

(a) Graph the function $ f(x) = \sin (\sin^{-1} x) $ and explain the appearance of the graph.
(b) Graph the function $ g(x) = \sin^{-1} (\sin x) $. How do you explain the appearance of this graph?

Answer

See explanations

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 3 Educators

Catherine R.

Caleb E.

Kristen K.

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

Catherine R.

Caleb E.

Kristen K.

Michael J.

Calculus 3 Bootcamp

Vectors Intro

Vector Basics - Example 1

Recommended Videos

Problem

(a) If we shift a curve to the left, what happens…

Problem 76 Hard Difficulty

(a) Graph the function $ f(x) = \sin (\sin^{-1} x) $ and explain the appearance of the graph.(b) Graph the function $ g(x) = \sin^{-1} (\sin x) $. How do you explain the appearance of this graph?

Answer

See explanations

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 3 Educators

Catherine R.

Caleb E.

Kristen K.

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

Catherine R.

Caleb E.

Kristen K.

Michael J.

Calculus 3 Bootcamp

Vectors Intro

Vector Basics - Example 1

Recommended Videos

(a) Graph the function $ f(x) = \sin (\sin^{-1} x) $ and explain the appearance of the graph.
(b) Graph the function $ g(x) = \sin^{-1} (\sin x) $. How do you explain the appearance of this graph?