If `f(x)=cos[pi^2]x +cos[-pi^2]x ,` where `[x]` stands for the greatest integer function, then (a)`f(pi/2)=-1` (b) `f(pi)=1` (c)`f(-pi)=0` (d) `f(pi/4)=1`

let f(x)=(sin4pi[x])/(1+[x]^(2)) , where px] is the greatest integer less than or equal to x then

Draw the graph of f(x) = cos pi[x] , where [*] represents the greatest integer function. Find the period of the function.

The range of sin^(-1)[x^2+1/2]+cos^(-1)[x^2-1/2] , where [.] denotes the greatest integer function, is {pi/2,pi} (b) {pi} (c) {pi/2} (d) none of these

f: Rvec[-1,oo)a n df(x)=1n([|s in2x|+|cos2x|]) (where [.] is the greatest integer function.) Then, (a) f(x)h a sr a ngZ (b) f(x)i sp e r iod i c function (c) f(x)i sin v e r t i b l ein[0,pi/4] (d) f(x) is into function

If f(x)=sin([x]pi)/(x^2+x+1) where [.] denotes the greatest integer function, then (A) f is one-one (B) f is not one-one and not constant (C) f is a constant function (D) none of these

The sum of roots of the equation cos^(-1)(cosx)=[x],[dot] denotes the greatest integer function, is (a) 2pi+3 (b) pi+3 (c) pi-3 (d) 2 pi-3

The function f(x)=(tan |pi[x-pi]|)/(1+[x]^(2)) , where [x] denotes the greatest integer less than or equal to x, is

find the range of function f(x)=sin(x+(pi)/(6))+cos(x-(pi)/(6))

If f(x)=(-1)^([2x/pi]),g(x)=|sinx|-|cosx|,a n dvarphi(x)=f(x)g(x) (where [.] denotes the greatest integer function), then the respective fundamental periods of f(x),g(x),a n dvarphi(x) are a) pi,pi,pi (b) pi,2pi,pi c) pi,pi,pi/2 (d) pi,pi/2,pi