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

Question

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

Smart Achievers · Accepted Answer

(4)

Ans. None of these

Explanation:

$x - [x] = 0$ 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.

Solution

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

1 1

2 2

3 3

4 None of these

Ans.
(4)

Ans. None of these

Explanation:

$x - [x] = 0$ 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.

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Solution

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

1 1

2 2

3 3

4 None of these

Ans. (4) Ans. None of these Explanation: 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.

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

Ans.
(4)

Ans. None of these

Explanation:

$x - [x] = 0$ 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.