# 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 7RE
To determine

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

Expert Solution

Solution:

The domain of the function h(x) is (6,).

The range of the function h(x) is (,).

### Explanation of Solution

Given:

The function h(x)=ln(x+6).

Calculation:

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

The function h(x)=ln(x+6) is defined when x+6>0.

Thus, x>6.

Hence, the function is defined for the numbers x>6.

Therefore, the domain of the function is (6,).

The range is the set of all output values of the function. So, find the output for the input values lies in the interval (6,).

Observe that as x gets closer to −6, but greater than −6, the value of h(x) approaches −∞.

Similarly, as x gets closer to −6, but greater than −6, the value of h(x) approaches ∞.

Thus, it can be concluded that the range of the function is (,).

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