Range of the function f(x)=log2⁡2−log2⁡16sin2⁡x+1 is :

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[0,1]

(−∞,1]

[−1,1]

(−∞,∞)

answer is B.

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Detailed Solution

f(x)=log2⁡2−2log2⁡16sin2⁡x+10≤log2⁡16sin2⁡x+1≤log2⁡17 ⇒2−2log2⁡17≤2−2log2⁡16sin2⁡x+1≤2⇒ 0<2−2log2⁡16sin2⁡x+1≤2⇒f(x)≤1

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