/*! 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. 38 In Problems 29 鈥� 44, for the g... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 38 (page 257)

In Problems 29 鈥� 44, for the given functions f and g, find:

(a)f鈭�g

(b)g鈭�f

(c)f鈭�f

(d) g鈭�g

State the domain of each composite function.

f(x)=xx+3g(x)=2x

Short Answer

Expert verified

a)f鈭�g=23x+2and its domain is:x|x鈮�0,x鈮�-23

b) g鈭�f=2(x+3)x, and its domain:x|x鈮�0,x鈮�-3

c)f鈭�f=x4x+9 and its domain is:x|x鈮�-3,x鈮�-94.

d)g鈭�g=x and its domain is:x|x鈮�0

Step by step solution

01

Step 1. Given information:

The functions are:

f(x)=xx+3g(x)=2x

The domain of f(x)={x|x鈮�-3}

The domain ofg(x)={x|x鈮�0}

02

Part (a)  Step 1. To find f∘g and its domain: 

f鈭�g=f(g(x))=2x2x+3=2x脳x2+3x=23x+2

This is defined when g(x)is defined and 3x+2鈮�0x鈮�-23

So the domain is:x|x鈮�-23,x鈮�0

03

Part (b)  Step 1. To find g∘fand its domain: 

g鈭�f=g(f(x))=2xx+3=2(x+3)x

This is defined when f(x)is defined andx鈮�0.

So domain is:localid="1648202205530" x|x鈮�-3,x鈮�0

04

Part (c)  Step 1. To find  and its domain: 

f鈭�f=f(f(x))=xx+3xx+3+3=xx+34x+9x+3=x4x+9

This is only defined when f(x)is defined and 4x+9鈮�0x鈮�-94

So domain is:x|x鈮�-3,x鈮�-49

05

Part (d)  Step 1. To find g∘g and its domain: 

g鈭�g=22x=x

This is defined when g(x)is defined.

So, domain is:x|x鈮�0

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

In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

f(x)=-3x+1x

Solve the equation3-x=81

and verify your results using a graphing utility.

The graph of an exponential function is given. Match each graph to one of the following functions.

Find the inverse of the functionf(x)=r2-x20鈮�x鈮�r

The domain of a one-to-one functiong is(-鈭�,0) , and its range is[0,鈭�). State the domain and the range ofg-1 .
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Statistics

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.