# To Express : The Function G ( x ) = ( 4 + x 3 ) 9 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 57E
To determine

## To Express : The Function G(x) = (4+x3)9 in the form f∘g∘h .

Expert Solution

The Final Answer is h(x)=x3 , g(x)=4+x and f(x)=x9 .

### Explanation of Solution

Given information : The function G(x) = (4+x3)9 is given.

Formula used : The concept of Combining Functions is used.

Calculation :

Since, the formula of G(x) says to add 4 to x3 and then take 9th power of it, we let,

h(x)=x3 , g(x)=4+x and f(x)=x9 .

Thus,

fgh(x)=f(g(h(x)))f(g(x3))f(4+x3) (4+ x 3 ) 9  =  G(x)

Hence, the functions h, g, f, are h(x)=x3 , g(x)=4+x and f(x)=x9 .

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