If f(x)=(sin([x]pi))/(x^2+x+1) , where [...

If `f(x)=(sin([x]pi))/(x^2+x+1)` , where `[dot]` denotes the greatest integer function, then

A

f is one-one

B

f is not one-one and non-constant

C

f is constant function

D

f is zero function

Verified by Experts

The correct Answer is:

C, D

`because sin([x]pi)=0`
`therefore f(x)=0" "[because[x]" is an integer"]`
implies f(x) is a constant function and also f(x) is a zero function.

Similar Questions

Explore conceptually related problems

If [x]^(2)-5[x]+6=0 , where [.] denotes the greatest integer function, then :

If f : R rarr R is a function defined by : f(x) = [x] c cos ((2x - 1)/(2))pi, where [x] denotes the greatest integer function, then 'f' is :

int_0^(pi) [cot x] dx , when [cdot] denotes the greatest integer function, is equal to :

lim_(x rarr oo) (log x)/([x]) , where [.] denotes the greatest integer function, is

lim_(xto0)[(-2x)/(tanx)] , where [.] denotes greatest integer function is

int_0^(2) [2x]dx = , where [.] denotes the greatest function.

The equation x^2 - 2 = [sin x], where [.] denotes the greatest integer function, has

lim_(x rarr oo) (logx^(n)-[x])/([x]) , where n in N and [.] denotes the greatest integer function, is