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 `x in (-oo,1/2)a n dY in (1/2,oo)` `x in (-oo in ,1/2)uu[0,oo)a n dY in (1/2,oo)` `X in (-oo,-1/2)uu[0,oo)a n dY in (1/2,oo)`

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

lim_(x->-1)1/(sqrt(|x|-{-x}))(w h e r e{x} denotes the fractional part of (x) ) is equal to (a)does not exist (b) 1 (c) oo (d) 1/2

Solution set of the inequation, (x^2-5x+6)/(x^2+x+1)<0 is x in (-oo,2) (b) x in (2,3) x in (-oo,2)uu(3,oo) (d) x in (3,oo)

If |x+2|lt=9 then x in (-7, 11) b. x in [-11 ,7] c. x in (-oo,7)uu(11 ,oo) d. x in (-oo,-7)uu[11 ,oo)

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)

Solution set of the inequation (x^2+4x+4)/(2x^2-x-1)>0, is x in (-oo,-2)uu(-2,1) x in (-oo,-2)uu(-2,-1/2)uu(1,oo) x in (-oo,-2)uu(-1/2,1)uu(1,oo) x in (-oo,1)

If x\ a n d\ a are real numbers such that a >0 and |x|> a , then (a) x in (-a ,oo) b. x in [-oo, a) c. x in (-a , a) d . x in (-oo,-a)U(a ,oo)

Let f(x)=[x]cos ((pi)/([x+2])) where [ ] denotes the greatest integer function. Then, the domain of f is (a) x epsilon R, x not an integer (b) x epsilon (-oo, -2)uu[-1,oo) (c) x epsilon R, x!=-2 (d) x epsilon (-oo,-1]

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

f(x)=(x-2)|x-3| is monotonically increasing in (a) (-oo,5/2)uu(3,oo) (b) (5/2,oo) (c) (2,oo) (d) (-oo,3)