Question Number 78449 by mathocean1 last updated on 17/Jan/20
$$\mathrm{find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{definition}\:\mathrm{of}\: \\ $$$$\mathrm{f}\left({x}\right)=\frac{−{x}}{\mid{x}\mid−{x}} \\ $$
Commented by Rio Michael last updated on 18/Jan/20
$${f}\left({x}\right)\:=\:\frac{{x}}{{x}−\mid{x}\mid} \\ $$$${so}\:{x}\:<\:\mathrm{0}\:{so}\:{that}\:{x}−\mid{x}\mid\:{should}\:{be}\: \\ $$$${defined}.\:{for}\:{example} \\ $$$${x}\:=−\:\mathrm{2},\:\:\:\:{x}−\mid{x}\mid\:=\:\:\mid−\mathrm{2}\mid−\left(−\mathrm{2}\right)\:=\:\mathrm{2}\:+\:\mathrm{4}\:=\:\mathrm{6} \\ $$$${so}\:\:{x}:\:{x}\:<\:\mathrm{0} \\ $$
Answered by key of knowledge last updated on 17/Jan/20
$$\mathrm{x}<\mathrm{0} \\ $$