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

Question

( A ) $[-\frac{\pi}{4}, \frac{\pi}{2})$
( B ) $[0, \pi]$
( C ) $[ 0, \frac{\pi}{2})$
( D ) $(-\frac{\pi}{2}, \frac{\pi}{2})$