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Question
Find the range of the following functions given by f(x) = 1 + 3 cos2x
(Hint: –1 ≤ cos 2x ≤ 1 ⇒ –3 ≤ 3 cos 2x ≤ 3 ⇒ –2 ≤ 1 + 3cos 2x ≤ 4)
Solution
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 1, we get
–2 ≤ 1 + 3cos 2x≤ 4
Or, –2 ≤ f(x) ≤ 4
Hence f(x) ∈ [–2, 4]
Therefore, the range of f = [–2, 4]
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