How can I identify the domain and range of problems such as sin(cos^-1(2x)) without using a calculator???

Other problems would be sin(sin^-1(x-1/2)) or cos^-1(2sin(x)).

Please help asap because I have a math test tomorrow and this is the only concept I do not know. (Headbang)(Headbang)(Headbang)(Headbang)

Thanks.