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The domain of the function $f (x) = \log 2 \sin x$ is

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R~{ nπ:n∈I }

R~{ nπ:n∈N }

∪ 2nπ,2n+1π

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detailed solution

Correct option is D

f(x) = log2 sin x is defined for all x forwhich sin x > 0. But sin x > 0 if x ∈ (0, π) ∪ (2π, 3π) ∪ …= ∪ 2nπ,2n+1π.

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The domain of the function f(x) = log2 sin x is

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The domain of the function $f (x) = \log 2 \sin x$ is