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Question Number 15082 by Tinkutara last updated on 07/Jun/17
The domain of f(x) = (√(x − 2{x})). (where {∙} denotes fractional part of x) is?
Thedomainoff(x)=x−2{x}.(where{⋅}denotesfractionalpartofx)is?
Answered by mrW1 last updated on 07/Jun/17
x=n+f {x}=f x−2{x}=n+f−2f=n−f≥0 n≥f if x>0: n≥f n≥1 ⇒x≥1 if x≤0: n≥f n=0 ⇒x>−1 ⇒x∈(−1,0] and [1,+∞) check: x=−0.5 x−2{x}=−0.5−2(−0.5)=0.5>0 x=1.5 x−2{x}=1.5−2×0.5=0.5>0
x=n+f{x}=fx−2{x}=n+f−2f=n−f⩾0n⩾fifx>0:n⩾fn⩾1⇒x⩾1ifx⩽0:n⩾fn=0⇒x>−1⇒x∈(−1,0]and[1,+∞)check:x=−0.5x−2{x}=−0.5−2(−0.5)=0.5>0x=1.5x−2{x}=1.5−2×0.5=0.5>0
Commented by Tinkutara last updated on 07/Jun/17
But answer is [2, ∞)
Butansweris[2,∞)
Commented by mrW1 last updated on 07/Jun/17
this answer is wrong. you can check with x=1.5 which is not in the range, but f(x)=(√((1.5)−2(0.5)))=(√(0.5)) ! ok
thisansweriswrong.youcancheckwithx=1.5whichisnotintherange,butf(x)=(1.5)−2(0.5)=0.5!ok

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