The domain of the function `f(x)=(1)/(sqrt(|cosx|+cosx))` is

Options

A. `[-2n pi, 2 n pi], n in Z`
B. `(2n pi,bar(2n+1) pi), n in Z`
C. `(((4n+1)pi)/(2),((4n+3)pi)/(2)), n in Z`
D. `(((4n-1)pi)/(2),((4n+1)pi)/(2)), n in Z`

Answer

D

Explanation

`|cosx|+cosx={(0",",cosx le 0),(2 cosx",",cosx gt 0):}`
For `f(x)` to be defined, `cos x gt 0`
or ` x in (((4n-1)pi)/(2),((4n+1)pi)/(2)), n in Z` (1st and 4th quadrant).