Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
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
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Heather Zimmers
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
02:20
Jeffrey Payo
Calculus 1 / AB
Calculus 2 / BC
Calculus 3
Chapter 1
Functions and Models
Section 5
Inverse Functions and Logarithms
Functions
Integration Techniques
Partial Derivatives
Functions of Several Variables
Johns Hopkins University
Campbell University
Oregon State University
Baylor University
Lectures
04:31
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.
12:15
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.
02:03
Explain how the graph of $…
02:24
Using the graph showna…
01:54
If you are given the graph…
01:43
Find (a) $f^{\circ} g$ and…
01:10
01:14
Find (a) $f \circ g$, (b) …
01:40
If $g(x)=\sqrt{f(x)},$ whe…
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.
View More Answers From This Book
Find Another Textbook