find the set of critical points for: 1: f (x) = (x/(⌊ x ⌋+⌊ −x⌋)) −x 2 : g(x) = (x/(⌊ x ⌋ +⌊ −x ⌋)) +x


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Question Number 184893 by mnjuly1970 last updated on 13/Jan/23

$f i n d t h e s e t o f$ $c r i t i c a l p o i n t s f o r :$ $1 : f (x) = \frac{x}{⌊ x ⌋ + ⌊ - x ⌋} - x$ $2 : g (x) = \frac{x}{⌊ x ⌋ + ⌊ - x ⌋} + x$
	Answered by Mathspace last updated on 13/Jan/23

	$1) x i n Z \Rightarrow [x] + [- x] = 0 \Rightarrow f i s n o t d e f i n e d$ $x \notin Z \Rightarrow [x] + [- x] = - 1 \Rightarrow$ $f (x) = \frac{x}{- 1} - x = - 2 x$ $a n y w a y w e h a v e D_{f} = R - Z$ $2) g (x) n o t d e f i n e d f o r x \in Z$ $a n d f o r x \notin Z g (x) = \frac{x}{- 1} + x = 0$ $\Rightarrow D_{g} = R - Z$
	Commented by mnjuly1970 last updated on 19/Jan/23

	$t h x a l o t$
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