If , f(x)= (x/(⌊ x ⌋)) ⇒ D_( f) =?(domain) and R


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Question Number 185054 by mnjuly1970 last updated on 16/Jan/23

$I f, f (x) = \frac{x}{⌊ x ⌋}$ $\Rightarrow D_{f} = ? (d o m a i n)$ $a n d R_{f} = ? (r a n g e)$
	Answered by mahdipoor last updated on 16/Jan/23
	$D_f =R−{x∈R,[x]=0}=R−[0,1) x=n+ε⇒y=(x/([x]))=((n+ε)/n)=1+(ε/n) −1<(ε/n)<1⇒0<y<2⇒R_f =(0,2)$
	$D_{f} = R - {x \in R, [x] = 0} = R - [0, 1)$ $x = n + ϵ \Rightarrow y = \frac{x}{[x]} = \frac{n + ϵ}{n} = 1 + \frac{ϵ}{n}$ $- 1 < \frac{ϵ}{n} < 1 \Rightarrow 0 < y < 2 \Rightarrow R_{f} = (0, 2)$
	Commented by mnjuly1970 last updated on 16/Jan/23

	$z e n d e h b s s h i d a l i b o o d . . .$
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