Home
Class 11
MATHS
We know that any real number x can be ex...

We know that any real number x can be expressed as followig `x=[x]+{x}`, where [x] is an integer and `0 le {x} lt 1`. We define [x] as the greatest integer less than or equal to x or integer part of x and [x] as the fractional part of x. Suppose for any real number x, we write `x=(x)-(x)`, where (x) is integer and `0 le (x) lt 1`. We define (x) as the least integer greater than (or) equal to x. For example `(3.26) =4(-14.4)= - 14(5)=5` elearly, if `x in I` then `(x)=[x]`. If `x !in I`, then `(x)=[x]+1` we can also define that `x in ( n , in +1) rArr (x)=n+1`, where `n in I`
The domain of defination of the function `f(x)=(1)/(sqrt(x-(x)))` is

A

I

B

`R-I`

C

`(0, oo)`

D

`phi`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Similar Questions

Explore conceptually related problems

We know that any real number x can be expressed as followig x=[x]+{x} , where [x] is an integer and 0 le {x} lt 1 . We define [x] as the greatest integer less than or equal to x or integer part of x and [x] as the fractional part of x. Suppose for any real number x, we write x=(x)-(x) , where (x) is integer and 0 le (x) lt 1 . We define (x) as the least integer greater than (or) equal to x. For example (3.26) =4(-14.4)= - 14(5)=5 elearly, if x in I then (x)=[x] . If x !in I , then (x)=[x]+1 we can also define that x in ( n , in +1) rArr (x)=n+1 , where n in I The range of the function f(x)=(1)/(sqrt((x)-[x])) is

If [x] denotes the greatest integer less than or equal to x then int_(1)^(oo) [(1)/(1+x^(2))]dx=

Show that the function defined by g(x) = x-[x] is a discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x.

Find all the points of discontinuity of the greatest interger function defined by f(x)= [x] , where [x] denote the greatest integer less than or equal to x.

Prove that the Greatest Integer Function f: R to R, given by f (x) =[x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

f(x)=(cos x)/([(2x)/(pi)]+1/2) , where x is not an integral multiple of pi and [.] denotes the greatest integer function, is

If [x] denotes the greatest integer lt x then the domain of the function function f(x) =sqrt((4-x^2)/([x]+2)) is

The function f(x)=(sec^(-1)x)/(sqrt(x-[x])) , where [x] denotes the greatest integer less or equal to x, is defined for all x in