# 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 30E
To determine

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

Expert Solution

The domain of the function is [2,3] ,

### Explanation of Solution

Given information:

The given function is,

f(x)=2x35x2+x6

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)=2x35x2+x6

The factors of denominator of the function is calculated as,

x2+x6=0x2+3x2x6=0(x+3)(x2)=0

The division by 0 is not allowed so The function f(x) is not defined when the denominator (x+3)(x2)0

The domain of f consists of all value of x

x+3=0x=3,x2=0x=2

Thus, the domain of f is

{x|x2,x3}

Therefore the domain of f is the interval,

[2,3]

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!