The range of the function \( f(x) = \log_{\sqrt{5}}\!\left( 3 + \cos\!\left(\frac{3\pi}{4} + x\right) + \cos\!\left(\frac{\pi}{4} + x\right) + \cos\!\left(\frac{\pi}{4} - x\right) - \cos\!\left(\frac{3\pi}{4} - x\right) \right) \) is:
\( \left[ \frac{1}{\sqrt{5}}, \, \sqrt{5} \right] \)
\( [0, \, 2] \)
\( [-2, \, 2] \)
\( (0, \, \sqrt{5}) \)
