# To Express : The Function G ( x ) = 2 ( 3 + x ) 2 in the form f ∘ g ∘ h . ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.6, Problem 58E
To determine

## To Express : The Function G(x)=2(3+x)2 in the form f∘g∘h .

Expert Solution

The Final Answer is h(x)=x , g(x)=(3+x)2 and f(x)=2x .

### Explanation of Solution

Given information : The function G(x)=2(3+x)2 is given.

Formula used : The concept of Combining Functions is used.

Calculation :

Since, the formula of G(x) says to add 3 to x and then square it and then divide 2 by it, so we let,

h(x)=x , g(x)=(3+x)2 and f(x)=2x .

Thus,

fgh(x)=f(g(h(x)))f(g(x))f((3+x)2)2(3+x)2= G(x)

Hence, the functions h, g, f, are h(x)=x , g(x)=(3+x)2 and f(x)=2x .

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