plz.. sir make me understand how the range of f(x)=x-[x]/1+x-[x] could be found out...where [x] den

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Expert Question: plz.. sir make me understand how the range of f(x)=x-[x]/1+x-[x] could be found out...where [x] den

Forum Index -> Differential Calculus

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9 Sep 2009 22:21:18 IST

Subject: plz.. sir make me understand how the range of f(x)=x-[x]/1+x-[x] could be found out...where [x]

Amy (20)

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plz.. sir make me understand how the range of f(x)=x-[x]/1+x-[x] could be found out...where [x] denotes greatest integer.

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29 Sep 2009 14:35:37 IST

Subject: plz.. sir make me understand how the range of f(x)=x-[x]/1+x-[x] could be found out...where [x]

Srujana (2785)

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$x-[x]=\{x\}$

$Let,\ y = \frac{\{x\}}{1+{\{x\}}}$

$\Rightarrow$ $\{x\}=\frac{y}{1-y}$

$0 \le \{x\} < 1$

$\Rightarrow$ $0 \le \frac{y}{1-y} < 1$

$\Rightarrow$ $y \ge 0,\ y<\frac{1}{2}$

$\Rightarrow$ $y\in \[0,\frac{1}{2}\)$

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