# The function f o g o h for functions f ( x ) = x 4 + 1 , g ( x ) = x − 5 and h ( x ) = x . ### 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 47E
To determine

## To find: The function fogoh for functions f(x)=x4+1 , g(x)=x−5 and h(x)=x .

Expert Solution

The function fogoh for functions f(x)=x4+1 , g(x)=x5 and h(x)=x is equal to (x5)4+1 .

### Explanation of Solution

Given information:

The functions are f(x)=x4+1 , g(x)=x5 and h(x)=x .

Calculation:

Simplify the function fogoh .

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

Substitute x for x in g(x)=x5 .

(fogoh)(x)=f(g(x))=f(x5)

Substitute x5 for x in f(x)=x4+1 .

(fogoh)(x)=f(x5)=(x5)4+1

Therefore, the function fogoh for functions f(x)=x4+1 , g(x)=x5 and h(x)=x is equal to (x5)4+1 .

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