First slide

Functions (XII)

Question

The domain of the function $\frac{1}{1 + 2 \sin x}$ is

Moderate

A

$R = \{n π + {(- 1)}^{n} \frac{7 π}{6}, n \in z\}$
B

$R = \{n π + {(- 1)}^{n} \frac{3 π}{6}, n \in z\}$
C

$R = \{n π + {(- 1)}^{n} \frac{5 π}{6}, n \in z\}$
D

$R = \{n π + {(- 1)}^{n} \frac{π}{6}, n \in z\}$

Solution

$T o d e f i n e f (x), w e m u s t h a v e$
$\begin{array}{l} 1 + 2 \sin x \neq 0 \\ or \sin x \neq - \frac{1}{2} or x \neq n π + (- 1)^{n} \frac{7 π}{6}, n \in Z \end{array}$
Hence, the domain of the function is
$R - \{n π + (- 1)^{n} \frac{7 π}{6}, n \in Z\}$

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