domain and range of inverse trig functions

hey, can someone tell me how to do these? like explain it and all

Find the domain and range of:

a) $\displaystyle y = 2tan^{-1}x$

do for y = 2tanx.. the domain would be -pi/2 < x < pi/2

the range is all real y

so for $\displaystyle y = 2tan^{-1}x $ to domain should be all real x

and range should be -pi/2 < x < pi/2

But the book said that the range should be -pi< x < pi

I don't get why.

b) $\displaystyle y=2cos^{-1}x - 1$

I don't understand this one at all

THANKS IN ADVANCE :)