MyQuestionIcon

1

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

Theorems for Continuity

If [ x 2]=[ x...

Question

If $[x^{2}] = [x + 2]$ , where [x] = the greatest integer less than or equal to x, then x must be such that

A

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

B

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

C

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

D

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

Open in App

Solution

The correct option is B
$[x^{2}] - [x] - 2 = 0$
$[x] = 2, - 1$
$\Rightarrow x ϵ [- 1, 0) \cup [2, 3)$

Suggest Corrections

thumbs-up

0

Similar questions

[x]^{2} = [x + 2]

[x] =

the greatest inetger less than or equal to

x

x

must be such that

Q. If the function

f : R \to R

f (x) = x - [x]

, where [x] denotes the greatest integer less than or equal to x, then

f^{- 1} (x)

\frac{1}{x - [x]}

(b) [x] − x

(c) not defined

(d) none of these

Q. If f(x) = sin [π²] x + sin [−π]² x, where [x] denotes the greatest integer less than or equal to x, then

(a) f(π/2) = 1
(b) f(π) = 2
(c) f(π/4) = −1
(d) None of these

If $f (x) = s i n [π^{2}] x + s i n [- π]^{2} x$ , where [x] denotes teh greatest integer less than or equal to x, then,

Q. Let [x] = greatest integer less than or equal to x and {x} = smallest integer greater than or equal to x. Then which of the following options is necessary true?

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Algebra of Continuous Functions

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Theorems for Continuity

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon