Spesh help!

[dave101]

Hi guys,

Need a bit of help on this question
Given that the domains of sin and cos are restricted to [−π/2 ,π/2] and [0,π] respectively,give the implied domain and range of each of the following:
y = cos(sin^−1 x)

Thanks a lot   

[fred42]

Domain of the inner function is [-1,1]
Range of the inner function is [-pi/2,pi/2]
Domain of the outer function is [0,pi]
Range of the outer function is [-1,1]

As this stands, the composite function doesn't exist, so the following changes need to be made:

Domain of the inner function is [-1,1]        change to [0,1] so that the range
Range of the inner function is [-pi/2,pi/2]  changes to [0,pi/2]
Domain of the outer function is [0,pi]        change to [0,pi/2] so that the range
Range of the outer function is [-1,1]         changes to [0,1]

Domain of composite function = [0,1] = Range

[dave101]

Thanks man!