MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Points of Discontinuity

The number of...

Question

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

A

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

none of these

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D none of these
The greatest integer function becomes discontinuous at every integer value of $x$ . So, the whole function will become discontinuous at each integer value of $x$ .
It has infinite number of points of discontinuity.

Suggest Corrections

thumbs-up

0

Similar questions

Q. The number of points at which the function

f (x) = \frac{1}{x - [x]}

is not continuous is
(a) 1
(b) 2
(c) 3
(d) none of these

f (x) = | x - 1 | + | x - 2 | + cos x

x \in [0, 4]

is not continuous at number of points

f (x) = | x - 1 | + | x - 2 | + cos x

x \in [0, 4]

is not continuous at number of points

Q. The set of points at which the function

f (x) = \frac{1}{\log |x|}

is not continuous, is ___________.

Q. The function

f (x) = \{\begin{cases} \frac{e^{1 / x} - 1}{e^{1 / x} + 1}, & x \neq 0 \\ 0, & x = 0 \end{cases}

(a) is continuous at x = 0
(b) is not continuous at x = 0
(c) is not continuous at x = 0, but can be made continuous at x = 0
(d) none of these

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Types of Discontinuity

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Points of Discontinuity

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon