First slide

Functions (XII)

Question

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

Moderate

A

$(- 2 nπ, 2 nπ)$
B

$(2 nπ, (2 n + 1) π)$
C

$((4 n - 1) \frac{π}{2}, (4 n + 1) \frac{π}{2})$
D

None of these

Solution

f (x) is defined if | sin x | + sin x > 0
$\begin{array}{l} \Rightarrow \sin x > 0 \Rightarrow 2 nπ < x < 2 nπ + π \\ ∴ Domain of f = (2 nπ, (2 n + 1) π) . \end{array}$

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