A) \[[0,\pi ]\]
B) \[\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]\]
C) \[\left[ 0,\frac{\pi }{2} \right)\]
D) None of these
Correct Answer: C
Solution :
Since, \[{{3}^{-{{x}^{2}}}}\]is defined for all \[x\in R,\] \[{{\cos }^{-1}}\left( \frac{x}{2}-1 \right)\] is defined for \[-1\le \frac{x}{2}-1\le 1\] ie, \[-2<x-2\le 2\,\,\,\,\,\,\Rightarrow \,\,\,\,\,0\le x\le 4\] and \[\log \,\cos \,x\] is defined for \[\cos \,x>0\] ie, \[2n\pi -\frac{\pi }{2}<x<2n\pi +\frac{\pi }{2}\] Hence, the largest interval lying in \[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)\]is \[\left[ 0,\frac{\pi }{2} \right)\].
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