Let f(x)=sqrt(|x|-{x})(w h e r e{dot} d...

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

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If f^(prime)(x)=|x|-{x}, where {x} denotes the fractional part of x , then f(x) is decreasing in (a) (-1/2,0) (b) (-1/2,2) (-1/2,2) (d) (1/2,oo)

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