A) \[-3\le x\le 3\]
B) \[-3<x<3\]
C) \[-9\le x\le 9\]
D) \[-9<x<9\]
E) \[-\infty <x<\infty \]
Correct Answer: B
Solution :
\[f(x)=\frac{1}{\sqrt{9-{{x}^{2}}}}\] For existence of \[f(x),\] \[9-{{x}^{2}}>0\] \[\Rightarrow \] \[{{x}^{2}}-9<0\] \[\Rightarrow \] \[(x-3)(x+3)<0\] \[\Rightarrow \] \[x\in (-3,3)\]or \[-3<x<3\] Which is the required domain of\[f(x)\].You need to login to perform this action.
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