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$The range of the function, f (x) = \cot^{- 1} \log_{0.5} (x^{4} - 2 x^{2} + 3) i s$

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(0,π)

(0,3π/4]

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[π/2,3π/4]

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detailed solution

Correct option is C

x4-2 x2+3 = x2-12+2 ≥2 ⇒logx4-2x2+3 0.5 ≤ log 2 0.5 =-log 2 2 =-1 since x≥y ⇒logx a ≤ logy a if 0

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The range of the function, f(x)=cot−1⁡log0.5⁡x4−2x2+3 is

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$The range of the function, f (x) = \cot^{- 1} \log_{0.5} (x^{4} - 2 x^{2} + 3) i s$