# The function f o g o h for functions f ( x ) = x , g ( x ) = x x − 1 and h ( x ) = x 3 .

### 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 48E
To determine

## To find: The function fogoh for functions f(x)=x , g(x)=xx−1 and h(x)=x3 .

Expert Solution

The function fogoh for functions f(x)=x , g(x)=xx1 and h(x)=x3 is equal to x3x31 .

### Explanation of Solution

Given information:

The functions are f(x)=x , g(x)=xx1 and h(x)=x3 .

Calculation:

Simplify the function fogoh .

(fogoh)(x)=(fog)(h(x))=(fog)(x3)=f(g(x3))

Substitute x3 for x in g(x)=xx1 .

(fogoh)(x)=f(g(x3))=f(x3x31)

Substitute x3x31 for x in f(x)=x .

(fogoh)(x)=f(x3x31)=x3x31

Therefore, the function fogoh for functions f(x)=x , g(x)=xx1 and h(x)=x3 is equal to x3x31 .

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