/*! 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} Q 54. In Problems 53鈥�58, find functi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q 54. (page 257)

In Problems 53鈥�58, find functionsf and g so that f鈭�g=H.

H(x)=(1+x2)3

Short Answer

Expert verified

The required functions aref(x)=x3;g(x)=1+x2

Step by step solution

01

Step 1. Given information. 

The given function is:

H(x)=(1+x2)3

In the given function H takes 1+x2and raises to the power 3.

Now decompose H by raising to the power 3.

Let's takeg(x)=1+x2andf(x)=x3

02

Step 2. Find f∘g.

(f鈭�g)(x)=f(g(x))

Substituteg(x)=1+x2 in the function f(g(x)),

Then the function will becomef(1+x2).

Now replace x with 1+x2in f(x)=x3,

f(1+x2)=(1+x2)3 (1+x2)3=H(x)

As we can see that f鈭�g=H, therefore the values of the function that we assumed are correct.

f(x)=x3;g(x)=1+x2

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

As the base a of an exponential function fx=ax, where a>1increases, what happens to the behavior of its graph forx>o?What happens to the behavior of its graph for x<0?

the function f is one-to-one. Find its inverse and check your answer.

f(x)=x2+33x2x>0

solve each equation. Verify your results using a graphing utility.

4x2=2x

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

For an exponential function, f(x)=Cax,f(x+1)f(x)=

Use the graph of y=f(x)given in the Problem 43to evaluate the following:

(a) f(-1)

(b) f(1)

(c) f-1(1)

(d) f-1(2)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

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.