A) \[(-\infty ,\ \infty )\]
B) \[(-\infty ,\ 3-\sqrt{3})\cup (3+\sqrt{3},\ \infty )\]
C) \[(-\infty ,\ 1]\cup [5,\ \infty )\]
D) \[[0,\ \infty )\]
Correct Answer: C
Solution :
The function \[f(x)=\sqrt{\log ({{x}^{2}}-6x+6)}\] is defined when \[\log ({{x}^{2}}-6x+6)\ge 0\] Þ \[{{x}^{2}}-6x+6\ge 1\] Þ \[(x-5)(x-1)\ge 0\] This inequality holds if \[x\le 1\] or \[x\ge 5\]. Hence, the domain of the function will be \[(-\infty ,\,1]\cup [5,\,\infty )\].
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