JEE Math Practice Question

The largest interval lying in $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$ for which the function $$f\left( x \right) = {4^{ - {x^2}}} + {\cos ^{ - 1}}\left( {{x \over 2} - 1} \right)$$$$ + \log \left( {\cos x} \right)$$, is defined, is

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