Let D be the domain of the function f(x)= sin^-1( log_3 x((6+2 log_3 x)/(-5 x))). If the range of the function g: D → R defined by g (x)=x-[x],([x]…

Let D be the domain of the function $\displaystyle f(x)=\sin ^{-1}\left(\log _{3 x}\left(\frac{6+2 \log _3 x}{-5 x}\right)\right)$. If the range of the function $\displaystyle \mathrm{g}: \mathrm{D} \rightarrow \mathbb{R}$ defined by $\displaystyle \mathrm{g}(x)=x-[x],([x]$ is the greatest integer function), is $\displaystyle (\alpha, \beta)$, then $\displaystyle \alpha^2+\frac{5}{\beta}$ is equal to