The domain of the function $$\cos^{-1}\left(\frac{2\sin^{-1}\left(\frac{1}{4x^2-1}\right)}{\pi}\right)$$ is

A

$$\left(-\infty, -\frac{1}{2}\right] \cup \left[\frac{1}{\sqrt{2}}, \infty\right) \cup \{0\}$$

B

$$\left(-\infty, -\frac{1}{\sqrt{2}}\right] \cup \left[\frac{1}{\sqrt{2}}, \infty\right)$$

C

$$\left(-\infty, -\frac{1}{\sqrt{2}}\right) \cup \left(\frac{1}{2}, \infty\right) \cup \{0\}$$

D

$$R - \left\{-\frac{1}{2}, \frac{1}{2}\right\}$$