# To Express : The Function F ( x ) = 1 x 2 + 1 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 55E
To determine

## To Express : The Function F(x)=1x2+1 in the form f∘g∘h .

Expert Solution

The Final Answer is h(x)=x2 , g(x)=x+1 and f(x)=1x .

### Explanation of Solution

Given information : The function F(x)=1x2+1 is given.

Formula used : The concept of Combining Functions is used.

Calculation :

Since, the formula of F(x) says to add 1 to x2 and then divide 1 by it, we let

h(x)=x2 , g(x)=x+1 and f(x)=1x .

Thus,

fgh(x)=f(g(h(x)))f(g(x2))f(x2+1)1x2+1= F(x)

Hence, the functions h, g, f, are h(x)=x2 , g(x)=x+1 and f(x)=1x .

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