A) \[NO\xrightarrow[{}]{{}}N{{O}^{+}}\]
B) \[{{O}_{2}}\xrightarrow[{}]{{}}O_{2}^{+}\]
C) \[\left[ -\frac{\pi }{4},\,\frac{\pi }{2} \right)\]
D) \[5f\]
Correct Answer: D
Solution :
\[{{4}^{-{{x}^{2}}}}\]is defined for\[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)\] \[{{\cos }^{-1}}\left( \frac{x}{2}-1 \right)\]is defined, if\[-1\le \frac{x}{2}-1\le 1.\] \[\Rightarrow \]\[0\le \frac{x}{2}\le 2\]\[\Rightarrow \]\[0\le x\le 4\] and\[log(cos\text{ }x)\] is defined, if \[cos\text{ }x>0\]. \[\Rightarrow \]\[-\frac{\pi }{2}<x<\frac{\pi }{2}\] Hence, \[f(x)={{4}^{-{{x}^{2}}}}+{{\cos }^{-1}}\left( \frac{x}{2}-1 \right)+\log (\cos x)\] is defined, if \[x\in \left[ 0,\,\frac{\pi }{2} \right)\]
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