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

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

$\left[ { - {\pi \over 4},{\pi \over 2}} \right)$

$\left[ {0,{\pi \over 2}} \right)$

$\left[ {0,\pi } \right]$

$\left( { - {\pi \over 2},{\pi \over 2}} \right)$

Solution

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