First slide

Functions (XII)

Question

The domain of the function $f (x) = \sqrt{\log (\frac{1}{|\sin x|})}$

Moderate

A

$R - \{- π, π\}$
B

$R - \{n π | n \in Z\}$
C

$R - \{2 n π | n \in z\}$
D

$(- \infty, \infty)$

Solution

$\begin{matrix} f (x) is defined for \\ \log (\frac{1}{|\sin x|}) \geq 0 \\ or \frac{1}{|\sin x|} \geq 1 and |\sin x| \neq 0 \\ or |\sin x| \neq 0 [\frac{1}{|\sin x|} \geq 1 for all x] \end{matrix}$
$\begin{array}{l} or x \neq n π, n \in Z \\ Hence, the domain of f (x) is R - \{n π . n \in Z\} . \end{array}$

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