# The domain and the range of the 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, Problem 6RE
To determine

## To find: The domain and the range of the function.

Expert Solution

Solution:

The domain of the function g(x) is [2,2].

The range of the function g(x) is [0,4].

### Explanation of Solution

Given:

The function g(x)=16x4.

Definition used:

The domain is the set of all input values of the function for which the function is real and defined.

Calculation:

Consider the expression 16x4.

Since the expression inside the radical cannot be negative, 16x40.

Thus, the undefined points are obtained follows:

16x416x4162x2

Thus, the solutions are, x=2 and x=2.

Hence, the function is undefined for x=2 and x=2.

Therefore, the domain of the function is [2,2].

The range is the set of all output values of the function. So, obtain the output for the input values lies in the interval [0,2].

If x=2, then g(x)=0.

If x=0, then g(x)=4.

If x0, then g(x)4.

If x=2, then g(x)=0.

Thus, it is observed that the range of the function is [0,4].

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