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)`

Options

A. ` x in (-oo,(1)/(2)]" and " Y in [(1)/(2), oo)`
B. ` x in (-oo, -(1)/(2)]cup [0,oo) " and " Y in [(1)/(2), oo)`
C. ` X in (-oo, -(1)/(2)]cup [0,oo) " and " Y in [0, oo)`
D. None of these

Answer

C

Explanation

`f(x)=sqrt(|x|-{x}) ` is defined if `|x| ge {x}`
or ` x in (-oo-(1)/(2)] cup [0,oo) " or " Y in [0,oo).`