Problem

(a) How is the logarithmic function $ y = \log_b …

01:55

Question

Answered step-by-step

Problem 32 Hard Difficulty

Let $ g(x) = \sqrt[3]{1 - x^3} $.

(a) Find $ g^{-1} $ . How is it related to $ g $?
(b) Graph $ g $. How do you explain your answer to part (a)?

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Heather Zimmers

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Johns Hopkins University

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

here we have function g of X, and we want to find its inverse. So let's start by re naming it as why. And then we're going to switch X and y. So now we have X equals the cube root of one minus y cubed. Now we want to solve for y isolate. Why? So we que both sides And then we subtract one from both sides. And then we could multiply both sides by negative one to get the wife cubed by itself. And finally to get why by itself we can cue brute both sides. And now, instead of calling it why we can call it g inverse of X. So let's take a look at what we have. G inverse of X is the cube root of one minus X cubed G of X was the cube root of one minus X cubed. They're exactly the same. Now let's take a look at the graph to understand why. So grabbing a graphing calculator going toe y equals we type in the function y equals a cube root of one minus X cubed and by the way, to find the cube root function, you can go to your math menu. There, you see it's number four, and I'm also going to graph y equals X just so I can see that reflection line. Now I'm going to go to Zoom Square for a good viewing window, and we can see that the graph that Cuba A graph is actually symmetric about the line y equals ax already, so it's just a reflection on itself.

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem

(a) How is the logarithmic function $ y = \log_b …

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 3 Educators

Lily An

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

Calculus 3 Courses

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

James Stewart

Calculus: Early Transcendentals

Lily An

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Lily An

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

James StewartCalculus: Early Transcendentals

Lily An

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

James Stewart

Calculus: Early Transcendentals