/*! 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 22. Find the domain of the composite... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q 22. (page 256)

Find the domain of the composite function f鈭�g.

f(x)=1x+3andg(x)=-2x.

Short Answer

Expert verified

Domain of composition of the functionf(x)=1x+3andg(x)=-2xis(-鈭�,0)鈭�(0,23)鈭�(23,鈭�).

Step by step solution

01

Step 1. Given information.

We have,

f(x)=1x+3andg(x)=-2x

02

Step 2. Concept used.

Domain is the set of all input values where the function is defined and real.

03

Step 3. Explanation.

We have,

f(x)=1x+3andg(x)=-2x

The function g(x) is well defined for all real values of x except x = 0.

So domain of the g(x) is all real numbers exceptx = 0.

Similarly domain of the f(x) is the set of all real numbers except x = -3.

So we need to exclude from the domain of g(x) that value of x for which g(x)=-3.

So -2x=-3

Solving it for x,

-2=-3x鈬�x=23

That is domain of the composite function of f(x)=1x+3andg(x)=-2xis the set of real numbers except x = 0 and x=23.

Domain:(-鈭�,0)鈭�(0,23)鈭�(23,鈭�)

04

Step 4. Conclusion.

Hence, domain of composite function of f(x)=1x+3andg(x)=-2xis(-鈭�,0)鈭�(0,23)鈭�(23,鈭�).

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

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 .

In Problems 33-40, the graph of an exponential function is given. Match each graph to one of the following functions.

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

True or False

To graph (x-2)3, shift the graph of y=x3to the left 2 units.

Findf(3x)iff(x)=4-2x2.

In Problems 33-40, the graph of an exponential function is given. Match each graph to one of the following functions.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Applied 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.