`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

Domain (D) and range (R) of f(x)=sin^(-1)(cos^(-1)[x]), where [.] denotes the greatest integer function, is

The range of f(x)=[|sin x|+|cosx"|""]"dot Where [.] denotes the greatest integer function, is {0} (b) {0,1} (c) {1} (d) none of these

Find the range of f(x)=(x-[x])/(1-[x]+x '),w h e r e[] represents the greatest integer function.

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

If f(x+2a)=f(x-2a),t h e np rov et h a tf(x)i sp e r iod i cdot

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

lim_(x->0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the greatest integer function). (a) -1 (b) 1 (c) 0 (d) does not exist

Find the period of the following. (i) f(x)=(2^(x))/(2^([x])) , where [.] represents the greatest integer function. (ii) f(x)=e^(sinx) (iii) f(x)=sin^(-1)(sin 3x) (iv) f(x) =sqrt(sinx) (v) f(x)=tan((pi)/(2)[x]), where [.] represents greatest integer function.

Find the domain and range of f(x)=sin^(-1)[x]w h e r[] represents the greatest function).

The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (where [.] represents the greatest integer function). -1 (b) 1 (c) 0 (d) none of these