The domain of the function $$f(x) = \sin^{-1}[2x^2 - 3] + \log_2\left(\log_{\frac{1}{2}}(x^2 - 5x + 5)\right)$$, where $$[t]$$ is the greatest integer function, is

A

$$\left(-\sqrt{\frac{5}{2}}, \frac{5-\sqrt{5}}{2}\right)$$

B

$$\left(\frac{5-\sqrt{5}}{2}, \frac{5+\sqrt{5}}{2}\right)$$

C

$$\left(1, \frac{5-\sqrt{5}}{2}\right)$$

D

$$\left[1, \frac{5+\sqrt{5}}{2}\right)$$