BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2.6, Problem 46E
To determine

To find: The function fogoh for functions f(x)=1x , g(x)=x3 and h(x)=x2+2 .

Expert Solution

Answer to Problem 46E

The function fogoh for functions f(x)=1x , g(x)=x3 and h(x)=x2+2 is equal to 1(x2+2)3 .

Explanation of Solution

Given information:

The functions are f(x)=1x , g(x)=x3 and h(x)=x2+2 .

Calculation:

Simplify the function fogoh .

  (fogoh)(x)=(fog)(h(x))=(fog)(x2+2)=f(g(x2+2))

Substitute x2+2 for x in g(x)=x3 .

  (fogoh)(x)=f(g(x2+2))=f((x2+2)3)

Substitute (x2+2)3 for x in f(x)=1x .

  (fogoh)(x)=f((x2+2)3)=1(x2+2)3

Therefore, The function fogoh for functions f(x)=1x , g(x)=x3 and h(x)=x2+2 is equal to 1(x2+2)3 .

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