Functions Question 532
Question: The domain of the function $ \sqrt{\log (x^{2}-6x+6)} $ is
[Roorkee 1999; MP PET 2002]
Options:
A) $ (-\infty ,\ \infty ) $
B) $ (-\infty ,\ 3-\sqrt{3})\cup (3+\sqrt{3},\ \infty ) $
C) $ (-\infty ,\ 1]\cup [5,\ \infty ) $
D) $ [0,\ \infty ) $
Show Answer
Answer:
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 ) $ .
BETA
