First slide

Functions (XII)

Question

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

Moderate

A

$[- 2 n π, 2 n π], n \in Z$
B

$(2 n π, \bar{2 n + 1} π), n \in Z$
C

$(\frac{(4 n + 1) π}{2}, \frac{(4 n + 3) π}{2}), n \in Z$
D

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

Solution

$|\cos x| + \cos x = 0 i f \cos x \leq 0$
$= 2 \cos x, i f \cos x > 0$
$f o r f (x) t o b e d e f i n e d, \cos x > 0 \Rightarrow x \in (\frac{(4 n - 1) π}{2}, \frac{(4 n + 1) π}{2}), n \in Z (i . e 1 s t a n d 4 t h q u a d r a n t s)$

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