# find the domain of the given function.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.1, Problem 29E
To determine

## To find: find the domain of the given function.

Expert Solution

The domain of the function is, (,3)(3,3)(3,)

### Explanation of Solution

Given information:

The given function is,

f(x)=x+4x29

Concept used:

To represent the function:

A function f is a rule that assigns to each element x in a set D exactly one element called f(x) in a set E. The set D and E are sets of real numbers. The set D is called the domain of the function.

If f is a function with domain D .

Then the set of ordered pairs are.

{(x,f(x))|xD}

The given function is

f(x)=x+4x29

The factors of denominator of the function is calculated as,

x29=x232=(x3)(x+3)

The function f(x) is not defined when the denominator (x+3)(x3)0

Thus, the domain of f is

{x|x3,x3}

Therefore the domain of f is the interval,

(,3)(3,3)(3,)

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