A) \[(-4,\,2)\]
B) \[(-4,\,\,4)\]
C) \[(-4,\,\,4]\]
D) \[[-4,\,\,4]\]
Correct Answer: A
Solution :
Given, \[f(x)=\sin \left\{ \log \,\,\left( \frac{\sqrt{16-{{x}^{2}}}}{2-x} \right) \right\}\] For \[f(x)\] to be defined, \[2-x>0\] and \[16-{{x}^{2}}>0\] \[\Rightarrow \] \[x<2\] and \[{{x}^{2}}<16\] \[\Rightarrow \] \[x<1\] and \[-4<x<4\] \[\Rightarrow \] \[-4<x<2\]
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