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Let f (x) be a function such that $f^{'} (x) = \log_{1 / 3} [\log_{3} (\sin x + a)]$ .If f(x) is decreasing for all real values of x, then

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a∈(1,4)

a∈[4,∞)

a∈(2,3)

a∈[2,∞)

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Correct option is B

We must have log1/3⁡log3⁡(sin⁡x+a)≤0∀x∈Ror log3⁡(sin⁡x+a)>1 ∀x∈Ror sin⁡x+a≥3 ∀x∈Ror a≥3−sin⁡x ∀x∈Ror a≥4

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Let f (x) be a function such that f′(x)=log1/3⁡log3⁡(sin ⁡x+a).If f(x) is decreasing for all real values of x, then

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Ready to Test Your Skills?

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Let f (x) be a function such that $f^{'} (x) = \log_{1 / 3} [\log_{3} (\sin x + a)]$ .If f(x) is decreasing for all real values of x, then