Find the domains of the following functions :
$f (x) = {log}_{x} sin x$

k π < x < (2 k + 1) π

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k π < x < (k - 1) π

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2 k π < x < (2 k + 1) π

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None of these

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Solution

The correct option is D $2 k π < x < (2 k + 1) π$
$sin x > 0$ and $x \neq 1$
Therefore, $2 k π < x < (2 k + 1) π$ but $, x \neq 1$ where $k$ is non-negative integer

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