Here's why:

* The cosine function itself: The cosine function, cos(x), has a range of [-1, 1]. This means its output values always fall between -1 and 1, inclusive.

* The effect of 2x: Multiplying the input of the cosine function by 2 (i.e., 2x) compresses the graph horizontally. However, it does not affect the range. The output values will still oscillate between -1 and 1.

Therefore, regardless of the value of x, the value of cos 2x will always be within the interval [-1, 1].