The number of points at which the function f ( x )=(1/ x -[ x ]),[.] denotes the greatest integer function is not continuous is

Question

The number of points at which the function f ( x )=(1/ x -[ x ]),[.] denotes the greatest integer function is not continuous is (A) 1 (B) 2 (C) 3 (D) None of these

Tardigrade Admin · Accepted Answer

x-[x]=0 when x is an integer, so that f(x) is discontinuous for all x ∈ I i.e., f ( x ) is discontinuous at infinite number of points.

Q. The number of points at which the function $f (x) = \frac{1}{x - [ x ]}, [.]$ denotes the greatest integer function is not continuous is

1

2

3

None of these

$x - [x] = 0$ when $x$ is an integer, so that $f (x)$ is discontinuous for all $x \in$ I i.e., $f (x)$ is discontinuous at infinite number of points.

Q. The number of points at which the function f(x)=x−[x]1​,[.] denotes the greatest integer function is not continuous is

1

2

3

None of these

x−[x]=0 when x is an integer, so that f(x) is discontinuous for all x∈ I i.e., f(x) is discontinuous at infinite number of points.

Q. The number of points at which the function $f (x) = \frac{1}{x - [ x ]}, [.]$ denotes the greatest integer function is not continuous is

$x - [x] = 0$ when $x$ is an integer, so that $f (x)$ is discontinuous for all $x \in$ I i.e., $f (x)$ is discontinuous at infinite number of points.