Functions Question 142
Question: Let $
[x] $ denotes the greatest integer less than or equal to x. If $ f(x)=[x\sin \pi x] $ , then $ f(x) $ is [IIT 1986]
Options:
A) Continuous at $ x=0 $
B) Continuous in $ (-1,0) $
C) Differentiable in (?1,1)
D) All the above
Show Answer
Answer:
Correct Answer: D
Solution:
Here, when $ -1\le x\le 1,0\le x\sin \pi x<1 $
$ \Rightarrow f(x)=[x,\sin \pi x]=0 $ for $ -1\le x\le 1,, $ i.e., $ f(x) $ is constant function (equal to zero) in $ [-1,1]. $
$ \Rightarrow f(x) $ is differentiable in $ (-1,1) $ .
BETA
