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 51E
To determine

To find: The functions f(x) and g(x) such that F(x)=x2x2+4 is equal to fog .

Expert Solution

Answer to Problem 51E

The functions f(x) and g(x) such that F(x)=x2x2+4 is equal to fog are xx+4 and x2 respectively.

Explanation of Solution

Given information:

The function is F(x)=x2x2+4 .

Calculation:

The function F(x)=x2x2+4 is quotient of x2 to the x2+4 .

So, take the functions f(x) equal to xx+4 and g(x) equal to x2 .

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

  (fog)(x)=f(g(x))=f(x2)=x2x2+4=F(x)

Therefore, the functions f(x) and g(x) such that F(x)=x2x2+4 is equal to fog are xx+4 and x2 respectively.

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