Functions Question 176
Question: At which points the function $ f(x)=\frac{x}{[x]} $ , where $ [.] $ is greatest integer function, is discontinuous
Options:
A) Only positive integers
B) All positive and negative integers and (0, 1)
C) All rational numbers
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
(i) When $ 0\le x<1 $ $ f(x) $ doesn’t exist as [x] = 0 here. (ii) Also $ \underset{x\to 1+}{\mathop{\lim }},f(x) $ and $ \underset{x\to 1-}{\mathop{\lim }},f(x) $ does not exist. Hence $ f(x) $ is discontinuous at all integers and also in (0, 1).
BETA
