Limits Continuity And Differentiability Question 24
Question: If function $ \text{f(x)=} \begin{cases} & \text{x,if x is rational} \\ & \text{1-x,if x is irrational} \\ \end{cases} .\text{,then} $ the number of points at which f(x) is continuous, is-
Options:
A) $ \infty $
B) 1
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ x=a\in Q;f(a)=a $
$ f({a^{+}})=1-a $
or $ a;f({a^{-}})=1 $
- a or a continuous at where $ 1-a=a\Rightarrow a=1/2 $
$ \Rightarrow $ continuous at one point.
BETA
