BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.3, Problem 39E
To determine

To find:the given function fgh .

Expert Solution

Answer to Problem 39E

  (fgh)(x)=x6+4x3+1 .

Explanation of Solution

Given:

The given function is f(x)=x3,g(x)=x2,h(x)=x3+2 .

Calculation:

As the given function is f(x)=2x1,g(x)=x2,h(x)=1x .

  (fgh)(x)=f(g(h(x)))=fx23{as g(x)=x2}=(x3+2)23{as h(x)=x3+2}=(x6+4x3+4)3=x6+4x3+1

Hence,the range and domain are (fgh)(x)=x6+4x3+1

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