Functions Question 54
If $ f(x)= \begin{cases} & \frac{x-|x|}{x},\quad\text{when } x\ne 0 \\ & 2, \quad\text{when } x=0 \\ \end{cases} $ , then
[AI CBSE 1982]
Options:
A) $ f(x) $ is continuous at $ x=0 $
B) $ f(x) $ is discontinuous at $ x=0 $
C) $ \underset{x\to 0}{\mathop{\lim }} f(x)=2 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to 0-}{\mathop{\lim }} f(x)=1+1=2,\underset{x\to 0+}{\mathop{\lim }} f(x)=0,f(0)=1$
BETA
