The domain of the function  $y=\sqrt[e]{\frac{2x-1}{2x^3+3x^2+x}}+\sqrt{{\sin }^{-1}\left({\log }_{2}x\right)}$ is

$y=\sqrt{\frac{2x-1}{2x^3+3x^2+x}}+\sqrt{{\sin }^{-1}\left({\log }_{2}x\right)}$

${\sin }^{-1}\left({\log }_{2}x\right)\ge 0$

$0\le {\log }_{2}x\le 1$

$1\le x\le 2$

$x\in [1,2]$

$\frac{2x-1}{x(2x+1)(x+1)}$

$x\in (-\infty ,-1)\cup (-\frac{1}{2},0)\cup [\frac{1}{2},\infty )$

$\therefore$ Common solution  $[\frac{1}{2},2)$