Find the range of the following functions given by f(x) = 1 + 3 cos 2x – InterviewSolution

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1.

Find the range of the following functions given by f(x) = 1 + 3 cos 2x

Answer»

Given that: f(x) = 1 + 3 cos 2x

We know that -1 ≤ cos 2x ≤ 1

⇒ -3 ≤ 3 cos 2x ≤ 3 ⇒ -3 + 1 ≤ 1 + 3 cos 2x ≤ 3 + 1

⇒ -2 ≤ 1 + 3 cos 2x ≤ 4 ⇒ -2 ≤ f(x) ≤ 4

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

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