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 9E
To determine

To determine the functions and their domains

Expert Solution

Answer to Problem 9E

The domain of f is {x|x0} and the domain of g is {x|x4} .

The functions are

  (f+g)(x)=2x+4x+4,(fg)(x)=2x4x+4,(fg)(x)=8x2+4x,(f/g)(x)=2x+84x

Explanation of Solution

Given information:

The given function is f(x)=2x,g(x)=4x+4 .

Formula used:

The formulas used are:

  (f+g)(x)=f(x)+g(x)(fg)(x)=f(x)g(x)(fg)(x)=f(x)g(x)(f/g)(x)=f(x)g(x)

Calculation :

The domain of f is {x|x0} and the domain of g is {x|x4} .

The functions f+g, fg, fg, f/g can be found by:

  (f+g)(x)=f(x)+g(x)    (f+g)(x)=2x+4x+4                    [domain {x|x0 and x4}](fg)(x)=f(x)g(x)    (fg)(x)=2x4x+4     [domain {x|x0 and x4}](fg)(x)=f(x)g(x)    (fg)(x)=(2x)(4x+4) (fg)(x)=8x2+4x    [domain {x|x0 and x4}](f/g)(x)=f(x)g(x)    (f/g)(x)=(2x)(4x+4)(f/g)(x)=2x+84x                      [domain {x|x0 and x4}]

Hence, the functions are

  (f+g)(x)=2x+4x+4,(fg)(x)=2x4x+4,(fg)(x)=8x2+4x,(f/g)(x)=2x+84x

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