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 6E
To determine

To determine the functions and their domains

Expert Solution

Answer to Problem 6E

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

Hence, the functions are

  (f+g)(x)=4x2+2x1,(fg)(x)=2x2+2x+1,(fg)(x)=3x4x2+6x32x,(f/g)(x)=x2+2x3x21

Explanation of Solution

Given information:

The given function is f(x)=x2+2x,g(x)=3x21 .

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|x0} .

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

  (f+g)(x)=f(x)+g(x)    (f+g)(x)=x2+2x+3x21(f+g)(x)=4x2+2x1       [domain {x|x0 and x0}](fg)(x)=f(x)g(x)    (fg)(x)=x2+2x3x2+1(fg)(x)=2x2+2x+1      [domain {x|x0 and x0}](fg)(x)=f(x)g(x)   (fg)(x)=(x2+2x)(3x21)(fg)(x)=3x4x2+6x32x     [domain {x|x0 and x0}](f/g)(x)=f(x)g(x)    (f/g)(x)=x2+2x3x21                 [domain {x|x0 and x0}]

Hence, the functions are

  (f+g)(x)=4x2+2x1,(fg)(x)=2x2+2x+1,(fg)(x)=3x4x2+6x32x,(f/g)(x)=x2+2x3x21

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