Find the range of the following functions given by

f (x) = 1 + 3 cos2x

Given: f (x) = 1 + 3 cos2x

To find: the range of 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

Given,

f (x) = 1 + 3 cos2x

We know the value of cos 2x lies between -1, 1, so

-1≤ cos 2x≤ 1

Multiplying by 3, we get

-3≤ 3cos 2x≤ 3

Adding with 1, we get

-2≤ 1 + 3cos 2x≤ 4

Or, -2≤ f(x)≤ 4

Hence f(x)∈ [-2, 4]

Hence the range of f = [-2, 4]