Question

Question #381c9

Answer 1

x can occupy values
`(-oo...........-5pi`to`-3pi`, `-3pi`to`-pi`,`-pi`to`pi`, `pi`to`3pi`,`3pi`to`5pi,.............oo)`

Explanation:

Given:
`f(x)=sqrtsin(cosx)`
requires that the number inside the square root to be positive
ie
`sin(cosx)>0`
The function sin is positive in first and second quadrant, thereby the values in third and fourth quadrant being prohibited

Further,
`cosx` can have 1 as the maximum value
and
cos x is positive in first and fourth quadrants
x can occupy values..........`-5pi`to`-3pi`, `-3pi`to`-pi`,`-pi`to`pi`, `pi`to`3pi`,`3pi`to`5pi`,............
ie`(-oo...........-5pi`to`-3pi`, `-3pi`to`-pi`,`-pi`to`pi`, `pi`to`3pi`,`3pi`to`5pi,.............oo)`