Question

Let f (x) = [x], where [x] denotes the greatest integer function contained in x. Consider the following statements:
(1) f(x) is not onto.
(2) f(x) is continuous at x = 0.
(3) f(x) is discontinuous for all positive integral values. Which of the statements given above are not correct?

• A. 1 and 2
• B. 1 and 3
• C. 2 and 3
• D. 1, 2 and 3

Answer 1

Answer: (B)

Function is $f (x) = [x]$, where $[x]$ denotes the greatest integer function contained in x.
$\therefore $ At $x = 0, f (x) = [x]$ is continuous and since $[x] \in I$ for $x \in I$ it is onto
So, 1 and 3 are not correct.