Published by:
CGP EDU Academic Team
Published on: August 12, 2026
The range of the function f (x) = 
is
Text Solution
Verified by ExpertsThe correct answer is:
D
Here (2 – log 2 (16 sin 2 x + 1) > 0 ⇒ 0 < 16 sin 2 x + 1 < 4
≤ sin 2 x < 
⇒ 1 ≤ 16 sin 2 x + 1 ≤ 4 ⇒ 0 ≤ log 2 (16 sin 2 x + 1) < 2
⇒ 2 ≥ 2 – log 2 (16 sin 2 x + 1) > 0
⇒ 
≥ 
(2 – log 2 (16 sin 2 x + 1)) > – ∞ ⇒ 2 ≥ y > – ∞
Hence range is y ∈ (– ∞, 2]
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