# The functions f ( x ) and g ( x ) such that F ( x ) = | 1 − x 3 | is equal to f o g .

### 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 53E
To determine

## To find: The functions f(x) and g(x) such that F(x)=|1−x3| is equal to fog .

Expert Solution

The functions f(x) and g(x) such that F(x)=|1x3| is equal to fog are |x| and 1x3 respectively.

### Explanation of Solution

Given information:

The function is F(x)=|1x3| .

Calculation:

The function F(x)=|1x3| is absolute value of 1x3 .

So, take the functions f(x) equal to |x| and g(x) equal to 1x3 .

Verify that (fog)(x)=F(x) .

(fog)(x)=f(g(x))=f(1x3)=|1x3|=F(x)

Therefore, the functions f(x) and g(x) such that F(x)=|1x3| is equal to fog are |x| and 1x3 respectively.

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