Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

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

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Heather Zimmers
Numerade Educator

Like

Report

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

More Answers

02:20

Jeffrey Payo

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Related Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Discussion

You must be signed in to discuss.
Top Calculus 3 Educators
Lily An

Johns Hopkins University

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Calculus 3 Courses

Lectures

Video Thumbnail

04:31

Multivariate Functions - Intro

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

Video Thumbnail

12:15

Partial Derivatives - Overview

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

Join Course
Recommended Videos

02:03

Explain how the graph of $…

02:24

Using the graph shown
a…

01:54

If you are given the graph…

01:43

Find (a) $f^{\circ} g$ and…

01:10

Explain how the graph of $…

01:14

Find (a) $f \circ g$, (b) …

01:40

If $g(x)=\sqrt{f(x)},$ whe…

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.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
162
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
70
Hosted by: Alonso M
See More

Related Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Top Calculus 3 Educators
Lily An

Johns Hopkins University

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Calculus 3 Courses

Lectures

Video Thumbnail

04:31

Multivariate Functions - Intro

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

Video Thumbnail

12:15

Partial Derivatives - Overview

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

Join Course
Recommended Videos

02:03

Explain how the graph of $g$ is obtained from the graph of $f$ a. $f(x)=\sqrt{x…

02:24

Using the graph shown a. Find $g(1)$ b. Solve $g(x)=1$ c. Find $g^{-1}(1)$ d. S…

01:54

If you are given the graph of $f(x)=a^{x},$ where $a>0$ and $a \neq 1$, how wou…

01:43

Find (a) $f^{\circ} g$ and $(b) g^{\circ} E$. $$f(x)=x^{3}-1, \quad g(x)=\sqrt[…

01:10

Explain how the graph of $g$ is obtained from the graph of $f$ a. $f(x)=x^{3}, …

01:14

Find (a) $f \circ g$, (b) $g \circ f,$ and (c) $g \circ g$. $$ f(x)=\sqrt[3]{x-…

01:40

If $g(x)=\sqrt{f(x)},$ where the graph of $f$ is shown, evaluate $g^{\prime}(3)$

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started