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 7E
To determine

To determine the functions and their domains

Expert Solution

Answer to Problem 7E

The domain of f is {x|2x2} and the domain of g is {x|x0} .

The functions are

  (f+g)(x)=4x2+1+x,(fg)(x)=4x21+x,(fg)(x)=(4x2)(1+x),(f/g)(x)=4x21+x

Explanation of Solution

Given information:

The given function is f(x)=4x2,g(x)=1+x .

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|2x2} 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)=4x2+1+x       [domain {x|2x2 and x0}](fg)(x)=f(x)g(x)    (fg)(x)=4x21+x     [domain {x|2x2 and x0}](fg)(x)=f(x)g(x)    (fg)(x)=(4x2)(1+x)      [domain {x|2x2 and x0}](f/g)(x)=f(x)g(x)    (f/g)(x)=4x21+x                      [domain {x|2x2 and x0 and x1}]

Hence, the functions are

  (f+g)(x)=4x2+1+x,(fg)(x)=4x21+x,(fg)(x)=(4x2)(1+x),(f/g)(x)=4x21+x

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