/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 33 Find (a) \(f \circ g,\) (b) \(g ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 33

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

Short Answer

Expert verified
The result for \(f \circ g\) and \(g \circ f\) is \(x\). For \(g \circ g\) the result is \((x^{3}+1)^{3}+1\).

Step by step solution

01

Finding \(f \circ g\)

Substitute \(g(x)\) into \(f(x)\) to obtain \(f(g(x)) = f(x^{3}+1)=\sqrt[3]{x^{3}+1-1} = \sqrt[3]{x^{3}}=x\).
02

Finding \(g \circ f\)

Substitute \(f(x)\) into \(g(x)\) yielding \(g(f(x)) = g(\sqrt[3]{x-1}) = (\sqrt[3]{x-1})^{3}+1=x-1+1=x\).
03

Finding \(g \circ g\)

Substitute \(g(x)\) into itself, looking for \(g(g(x)) = g(x^{3}+1)= (x^{3}+1)^{3}+1\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) Write the linear function \(f\) such that it has the indicated function values and (b) Sketch the graph of the function. $$f(-5)=-1, \quad f(5)=-1$$

Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(y\) varies inversely as \(x .(y=3 \text { when } x=25 .)\)

(a) use a graphing utility to graph the function and (b) state the domain and range of the function. $$k(x)=4\left(\frac{1}{2} x-\left[\left[\frac{1}{2} x\right]\right]\right)^{2}$$

Find the difference quotient and simplify your Answer: $$f(x)=x^{3}+3 x, \quad \frac{f(x+h)-f(x)}{h}, \quad h \neq 0$$

Consider \(f(x)=\sqrt{x-2}\) and \(g(x)=\sqrt[3]{x-2}\) Why are the domains of \(f\) and \(g\) different?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.