Functions Question 263
Question: The domain of the function $ f(x)=\frac{{{\sin }^{-1}}(3-x)}{\ln (|x|\ -2)} $ is
[Orissa JEE 2002]
Options:
A) [2, 4]
B) (2, 3) È (3, 4]
C) [2, $ \infty $ )
D) $ (-\infty ,\ -3)\cup [2,\ \infty ) $
Show Answer
Answer:
Correct Answer: B
Solution:
$ f(x)=\frac{{{\sin }^{-1}}(3-x)}{\log [ |x|-2 ]} $ Let $ g(x)={{\sin }^{-1}}(3-x) $
Þ $ -1\le 3-x\le 1 $ Domain of $ g(x) $ is [2, 4] and let $ h(x)=\log [ |x|-2 ] $
Þ $ |x|-2>0 $
Þ $ |x|,>2 $
Þ $ x<-2 $ or $ x>2 $
Þ $ (-\infty ,,-2)\cup (2,,\infty ) $ we know that $ (f/g)(x)= $ $ \frac{f(x)}{g(x)}\forall x\in D_1\cap D_2-{ x\in R:g(x)=0 } $ \ Domain of $ f(x)=(2,,4]-{3} $ $ =(2,,3)\cup (3,,4] $ .
BETA
