question_answer

If  then the value of \[f[2x]\] 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

where \[[.]\] greatest integer function.

\[\Rightarrow \,\,f(x),\]for all values of x where \[x<1/2\] continuous function and for \[x=1/2\]and \[x=1,\]\[f(x)\] be a discontinuous function. So, answer [d] is correct.