question_answer

If   then \[f(\left| 2x \right|)\] will be (where [   ] shows the greatest integer function]

A) Continuous at \[x=-1\]

B) Continuous at \[x=0\]

C) Discontinuous at \[x=\frac{1}{2}\]

D) All of these

Correct Answer: D

Solution :

and

\[\Rightarrow \]\[f(\left| 2x \right|)\]is continuous function for all values of x where \[x<\frac{1}{2}\] and for \[x=\frac{1}{2}\]and \[x=1,f(\left| 2x \right|)\]is a discontinuous function.