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

A

$$135$$

B

$$45$$

C

$$46$$

D

$$136$$