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

Let f(x)=sqrt([sin 2x] -[cos 2x]) (where I I denotes the greatest integer function) then the range of f(x) will be

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

Check the nature of the following function. (i) f(x)=sin x, x in R " (ii) " f(x) =sin x, x in N

If f(x)=x^m n ,n in N , is an even function, then m is even integer (b) odd integer any integer (d) f(x)-e v e ni snotpos s i b l e

Statement 1: f(x)=cos x is continous at x=0a n dg(x)=[tanx],"w h e r e"[dot] represents greatest integer function, is discontinuous at x=0,t h e nh(x)=f(x)dotg(x) is discontinuous at x=0. Statement 2: If f(x) is continous and g(x) is discontinuous at x=a ,t h e nh(x)=f(x)g(x) is discontinuous at x=a

L e tf:[1,oo)->Ra n df(x)=int_1^x(e^t)/t dt-e^xdotT h e n f(x) is an increasing function lim_(x->oo)f(x)->oo f^(prime)(x) has a maxima at x=e f(x) is a decreasing function

The area bounded by the curve f(x)=x+sinx and its inverse function between the ordinates x=0a n dx=2pi is 4pis qdotu n i t s (b) 8pis qdotu n i t s 4s qdotu n i t s (d) 8s qdotu n i t s

If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

If f(x)= (x^m)^(1/n) ,n in N , is an even function, then m is (a)even integer (b) odd integer (c) any integer (d) f(x)-e v e ni s not pos s i b l e