question_answer

Let \[f(x)=Max\] \[\{[x],|x|\},\] then \[f(x)\] is discontinuous at [Note: [x] denotes the greatest integer less than or equal to x]

A)  \[x=0\]                 

B) no point             

C) \[x=n,\text{ }n\text{ }\in \text{ }N\]    

D) \[x=k,\,k\in I\]

Correct Answer: B

Solution :

[b] \[f(x)=Max.\] \[\{[x],\,|x|\}=|x|\forall x\in R\] Clearly, \[f(x)\] is discontinuous at no point.