# 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 8RE
To determine

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

Expert Solution

Solution:

The domain of the function F(t) is (,).

The range of the function F(t) is [2,4].

### Explanation of Solution

Given:

The function F(t)=3+cos2t.

Definition used:

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

Calculation:

Recall the fact that the domain of the cosine function is (,) and the range [1,1].

Note that the adding 3 to the cosine function does not change the domain.

Thus, domain of the function F(t)=3+cos2t is (,).

The range of the cosine function is [1,1].

That is, 1cos2t1.

For 3+cos2t, the range of the function is obtained as follows.

1+3cos2t+31+32cos2t+34

Thus, it can be concluded that the range of the function is [2,4].

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