A) \[[-1,\,1]\]
B) \[[1,\,\infty )\]
C) \[(-\infty ,\,-1]\]
D) \[(-\infty ,\,-1]\cup [1,\infty )\]
Correct Answer: D
Solution :
\[f(x)=\sqrt{{{\log }_{10}}{{x}^{2}}}\]is real. If \[{{\log }_{10}}{{x}^{2}}\ge 0\] \[\Rightarrow \] \[{{x}^{2}}\ge 1\] \[\Rightarrow \] \[x<-1\]and \[x>1\] \[\Rightarrow \] \[x\in (-\infty ,-1]\cup [1,\infty )\]
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