# the functions and their domains

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.6, Problem 10E
To determine

## To determine the functions and their domains

Expert Solution

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

The functions are

(f+g)(x)=2+xx+1,(fg)(x)=2xx+1,(fg)(x)=2xx2+2x+1,(f/g)(x)=2x+2x2+x

### Explanation of Solution

Given information:

The given function is f(x)=2x+1,g(x)=xx+1 .

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|x1} and the domain of g is {x|x1} .

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

(f+g)(x)=f(x)+g(x)    (f+g)(x)=2x+1+xx+1(f+g)(x)=2+xx+1                    [domain {x|x1 and x1}](fg)(x)=f(x)g(x)    (fg)(x)=2x+1xx+1(fg)(x)=2xx+1             [domain {x|x1 and x1}](fg)(x)=f(x)g(x)    (fg)(x)=(2x+1)(xx+1) (fg)(x)=2xx2+2x+1    [domain {x|x1 and x1}](f/g)(x)=f(x)g(x)    (f/g)(x)=(2x+1)(xx+1)(f/g)(x)=2x+2x2+x                      [domain {x|x1 and x1 and x0}]

Hence, the functions are

(f+g)(x)=2+xx+1,(fg)(x)=2xx+1,(fg)(x)=2xx2+2x+1,(f/g)(x)=2x+2x2+x

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