# Find the domain of the function g ( x ) = 2 + x 3 − x

### 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 2.1, Problem 57E
To determine

## Find the domain of the function g(x)=2+x3−x

Expert Solution

The domain of the function g(x)=2+x3x is [2,3)(3,)

### Explanation of Solution

Given information: Consider the function g(x)=2+x3x

Calculation:

We can’t take the square root of a negative number, so we must have g(x)0

2+x0x2

And for denominator,

A rational expression is not defined when the denominator is 0.

Since 3x0

x3

Hence the given function is defined for all the values of x in the set of real numbers except of the value x=3

Thus, the domain of the function g(x)=2+x3x is [2,3)(3,)

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