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Let f(x)=sqrt(|x|-{x}), where {.} denote...

Let `f(x)=sqrt(|x|-{x})`, where `{.}` denotes the fractional part of x an X,Y and its domain and range respectively, then

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

Text Solution

Verified by Experts

The correct Answer is:
C
`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).`
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