Functions Question 578
Question: The domain of the function $ f(x)=\frac{1}{{\log_{10}}(1-x)}+\sqrt{x+2} $ is
[DCE 2000]
Options:
A) $ ]-3,\ -2.5[\cup ]-2.5,\ -2[ $
B) $ [-2,\ 0[\cup ]0,\ 1[ $
C) ]0,1[
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ x+2\ge 0 $ i.e., $ x\ge -2\text{ or }-2\le x $
$ \because {\log_{10}}(1-x)\ne 0 $
Þ $ 1-x\ne 1 $
Þ $ x\ne 0 $
Again $ 1-x>0 $
Þ $ 1>x $
Þ $ x<1 $
All these can be combined as $ -2\le x<0 $
and $ 0<x<1 $ .
BETA
