# 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 33E
To determine

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

Expert Solution

The domain of the function is, (,0)(5,)

### Explanation of Solution

Given information:

The given function is,

h(x)=1x25x4

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

h(x)=1x25x4

The fourth root a negative number is not allowed (as a real number)

That h(x) is not defined when x25x0

The domain of h consists of all value of x such that

x25x0x25x>0x(x5)>0

There are two conditions,

First condition,

x>0

And,

x5>0x>5

Second condition,

x<0

And,

x5<0x<5

Hence, the domain of h is

{xR|x0,x5}

Therefore the domain of h is the interval,

(,0)(5,)

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