JEE Math Practice Question

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

1. A.$$ \left(-\sqrt{\frac{5}{2}}, \frac{5-\sqrt{5}}{2}\right) $$
2. B.$$ \left(\frac{5-\sqrt{5}}{2}, \frac{5+\sqrt{5}}{2}\right) $$
3. C.$$ \left(1, \frac{5-\sqrt{5}}{2}\right) $$
4. D.$$ \left[1, \frac{5+\sqrt{5}}{2}\right) $$