Functions Question 349
Question: The domain of the function $ f(x)=\log (\sqrt{x-4}+\sqrt{6-x}) $ is
[RPET 2001]
Options:
A) $ [4,\infty ) $
B) $ (-\infty ,\ 6] $
C) $ [4,\ 6] $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x)=\log (\sqrt{x-4}+\sqrt{6-x}) $
Þ $ y=x^{x},\Rightarrow ,\log y=x\log x $ and $ 6-x\ge 0 $
Þ $ x\ge 4 $ and $ x\le 6 $
$ \therefore $ Domain of
$ \therefore \underset{y\to 0}{\mathop{\lim }}\log y=\underset{x\to 0}{\mathop{\lim }},x\log x $ = $ [0] $ .
BETA
