For relation `2logy-logx-log(y-1)` a. Domain `=[4,+oo)`,range-`(1,+oo)` b. Domain `=[4,+oo),` range- `(2,+oo)` c. Domain `=(2,+oo)` ,range-`(2,+oo)` d. None of these

The domain and range of the real function f defined by f(x)=(4-x)/(x-4) is (a) Domain =R , Range ={-1,2} (b) Domain =R -{1}, Range R (c) Domain =R -{4}, Range ={-1} (d) Domain =R -{-4}, Range ={-1,1}

Let f(x)=sqrt(|x|-{x})(w h e r e{dot} denotes the fractional part of (x)a n dX , Y are its domain and range, respectively). Then (a) X in (-oo,1/2) and Y in (1/2,oo) (b) X in (-oo in ,1/2)uu[0,oo)a n dY in (1/2,oo) (c) X in (-oo,-1/2)uu[0,oo)a n dY in [0,oo) (d) none of these

If (|x-2|)/(x-2)geq0, then x in [2,oo) b. x in (2,oo) c. x in (-oo,2) d. x in (-oo,2]

The domain of the function f(x)=sqrt(((x+1)(x-3))/(x-2)) is [-1,2)uu[3,oo) b. (-1,2)uu[3,oo) c. [-1,2]uu[3,oo) d. none of these

The domain of the function f(x)=((x+1)(x-3))/(x-2) is a. [-1,2)uu[3,oo) b. (-oo,-3)uu(2,5) c. (-oo,-3]uu[2,5] d. none of these

The domain of f(x)="log"|logx|i s (0,oo) (b) (1,oo) (c) (0,1)uu(1,oo) (d) (-oo,1)

If (log)_3(x^2-6x+11)lt=1, then the exhaustive range of values of x is: (a) (-oo,2)uu(4,oo) (b) (2,4) (c) (-oo,1)uu(1,3)uu(4,oo) (d) none of these

If |x-1|>5, then a. x in (-4,6) b. x in [-4,6] c. x in (-oo,-4)uu(6,oo) d. x in (-oo,-4)uu[6,oo)

For x^2-(a+3)|x|=4=0 to have real solutions, the range of a is a (-oo,-7]uu[1,oo) b (-3,oo) c (-oo,-7] d [1,oo)

If domain of f(x) be (-1, 2), then (1) domain of f(sin x) will be (-oo, oo) (2) domain of f(ln x) will be (1/e, e^2) (3) domain of f(2x-3) will be (1,5/2) (4) domain of f([x]) will be [0, 2), where [x]<=x