Range of is

Given:

To find: the range of the given function

Explanation: So the range of a function consists of all the second elements of all the ordered pairs, i.e., f(x), so we have to find the values of f(x) to get the required range

We know the value of cos x lies between -1, 1, so

-1≤ cos x≤ 1

Multiplying by 2, we get

-2≤ 2cos x≤ 2

Adding a negative sign, we get

2≥ -2cos x≥ -2

Adding with 1, we get

3≥ 1-2cos x≥ -1

Now is defined if

-1≤ 1- 2 cos x < 0 or 0 < 1- 2 cos x ≤ 3

So the correct answer is option (C)