# How do you find the domain and range of (1/2)cos2x?

##### 1 Answer
Oct 8, 2017

The domain is $x \in \mathbb{R}$
The range is $y \in \left[- \frac{1}{2} , \frac{1}{2}\right]$

#### Explanation:

The domain of the $\cos \left(2 x\right)$ is $x \in \mathbb{R}$

To calculate the range, proceed as follows

Let $y = \frac{1}{2} \cos \left(2 x\right)$

$- 1 \le \cos \left(2 x\right) \le 1$

and

$- \frac{1}{2} \le \frac{1}{2} \cos \left(2 x\right) \le \frac{1}{2}$

$- \frac{1}{2} \le y \le \frac{1}{2}$

The range is $y \in \left[- \frac{1}{2} , \frac{1}{2}\right]$