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

Mr F says: There's a dilation by a factor of 2 in the vertical direction therefore the range is $\displaystyle {\color{red}2 \left(-\frac{\pi}{2}\right) < x < 2 \left(\frac{\pi}{2}\right) \Rightarrow -\pi < x < \pi}$.
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