Question

The function $f(x)=[x]$ where $[x]$ denotes the greatest integer not greater than $x,$ is _____

• A. continuous for all real values of x
• B. continuous only at rational values of x
• C. continuous for all non integral values of x
• D. continuous only at positive integral values of x

Answer 1

Answer: (C)

Given, $f(x)=[x]$ from the graph we observe that $f(x)=[x]$ discontinuous at every integral value of $x.$
That means, $f(x)=[x].$
Continuous only for all non-integral values of $x$.