JEE Math Practice Question

The range of the function, $$f(x) = {\log _{\sqrt 5 }}\left( {3 + \cos \left( {{{3\pi } \over 4} + x} \right) + \cos \left( {{\pi \over 4} + x} \right) + \cos \left( {{\pi \over 4} - x} \right) - \cos \left( {{{3\pi } \over 4} - x} \right)} \right)$$ is :

1. A.$$\left( {0,\sqrt 5 } \right)$$
2. B.[$$-$$2, 2]
3. C.$$\left[ {{1 \over {\sqrt 5 }},\sqrt 5 } \right]$$
4. D.[0, 2]