The largest interval lying in $\left( { - \frac{\pi }{2},\frac{\pi }{2}} \right)$ for which the function, $f\left( x \right) = {4^{ - {x^2}}} + {\cos ^{ - 1}}\left( {\frac{x}{2} - 1} \right) + \log \left( {\cos x} \right)$ is defined is
The largest interval lying in $\left( { - \frac{\pi }{2},\frac{\pi }{2}} \right)$ for which the function, $f\left( x \right) = {4^{ - {x^2}}} + {\cos ^{ - 1}}\left( {\frac{x}{2} - 1} \right) + \log \left( {\cos x} \right)$ is defined is
- [AIEEE 2007]
- A
$\left[ { - \frac{\pi }{4},\frac{\pi }{2}} \right)$
- B
$\left[ {0,\frac{\pi }{2}} \right)$
- C
$\left[ {0,\pi } \right]$
- D
$\;\left( { - \frac{\pi }{2},\frac{\pi }{2}} \right)$
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