what is the domain of sine inverse 2x

As in sin^-1x has  x belongs to -1 to 1
Hence in sin^-12x  , 2x belongs to -1 to 1 , as for 2x the domain remains same
 $$\begin{gathered} -1\le 2x\le 1 \\ Or \frac{-1}{2}\le x\le \frac{1}{2} \end{gathered}$$
Hence the domain is [-1/2 , 1/2]