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?

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

Tardigrade Admin · Accepted Answer

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

Q. 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?

1 and 2

1 and 3

2 and 3

1, 2 and 3

Function is $f (x) = [x]$ , where $[x]$ denotes the greatest integer function contained in x.
$∴$ 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.

Q. 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?