Let $$[\cdot]$$ denote the greatest integer function. If the domain of the function $$f(x) = \sin^{-1}\left(\frac{x + [x]}{3}\right)$$ is $$[\alpha, \beta)$$, then $$\alpha^2 + \beta^2$$ is equal to:

A

2

B

5

C

10

D

13