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 8E
To determine

To determine the functions and their domains

Expert Solution

Answer to Problem 8E

The domain of f is {x|3x3} and the domain of g is {x|2x2} .

The functions are

  (f+g)(x)=9x2+x24,(fg)(x)=9x2x24,(fg)(x)=(9x2)(x24),(f/g)(x)=9x2x24

Explanation of Solution

Given information:

The given function is f(x)=9x2,g(x)=x24 .

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|3x3} and the domain of g is {x|2x2} .

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

  (f+g)(x)=f(x)+g(x)    (f+g)(x)=9x2+x24       [domain {x|3x3 and 2x2}](fg)(x)=f(x)g(x)    (fg)(x)=9x2x24     [domain {x|3x3 and 2x2}](fg)(x)=f(x)g(x)    (fg)(x)=(9x2)(x24)      [domain {x|3x3 and 2x2}](f/g)(x)=f(x)g(x)    (f/g)(x)=9x2x24                      [domain {x|3x3 and 2x2 and x0}]

Hence, the functions are

  (f+g)(x)=9x2+x24,(fg)(x)=9x2x24,(fg)(x)=(9x2)(x24),(f/g)(x)=9x2x24

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