For any real number x- -x2-x-32- - where - - denotes the greatest integer function-

Given: [x2]+[x+32] =[x2]+[x+1+22] =[x2]+[x+12+1] Using [x± n ]=[x]± n wheren∈ℤ ⇒[x2]+[x+32]=[x2]+[x+12]+1 Using [x2]+[x+12]=[x] ∀ x∈ℝ, ⇒[x2]+[x+32]=[x]+1 =[x+1 ...

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

Byju's Answer

For any real ...

Question

For any real number $x, [\frac{x}{2}] + [\frac{x + 3}{2}] =$ , where $[.]$ denotes the greatest integer function.

[x] + 2

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

[x + 1]

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

[2 x + 1]

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

Open in App

Solution

The correct option is B $[x + 1]$
Given: $[\frac{x}{2}] + [\frac{x + 3}{2}]$
$= [\frac{x}{2}] + [\frac{x + 1 + 2}{2}] = [\frac{x}{2}] + [\frac{x + 1}{2} + 1]$
Using $[x \pm n] = [x] \pm n$ where $n \in Z$
$\Rightarrow [\frac{x}{2}] + [\frac{x + 3}{2}] = [\frac{x}{2}] + [\frac{x + 1}{2}] + 1$
Using $[\frac{x}{2}] + [\frac{x + 1}{2}] = [x] \forall x \in R,$
$\Rightarrow [\frac{x}{2}] + [\frac{x + 3}{2}] = [x] + 1 = [x + 1]$

Suggest Corrections

Similar questions

Q. For any real number

x,

such that

a \leq x < a + 1, [x] = a .

Where [.] is the greatest integer function.

[x] = x

for any integral value of

x

, where

[x]

denotes the greatest integer function.

Q. The number of real solutions of the equation

| x - 5 | = [- 2 π] + [e^{2}]

is (where [.] denotes greatest integer function)

Q. Let

f (x) = | [x] x |

for

- 1 \leq x \leq 2

, where

[x]

denotes greatest integer function, then

Q. Let

x

be a real number

[x]

denotes the greatest integer function, and

{x}

denotes the fractional part and

(x)

denotes the least integer function,then solve the following.

{[x]}^{2} + 2 [x] = 3 x, 0 \leq x \leq 2

Join BYJU'S Learning Program

For any real number x,[x2]+[x+32]= , where [ .] denotes the greatest integer function.

The correct option is B [x+1]Given: [x2]+[x+32] =[x2]+[x+1+22]=[x2]+[x+12+1] Using [x±n]=[x]±n wheren∈Z ⇒[x2]+[x+32]=[x2]+[x+12]+1 Using [x2]+[x+12]=[x] ∀ x∈R, ⇒[x2]+[x+32]=[x]+1=[x+1]

For any real number $x, [\frac{x}{2}] + [\frac{x + 3}{2}] =$ , where $[.]$ denotes the greatest integer function.