Question Number 12495 by shardon last updated on 23/Apr/17
$${find}\:{the}\:{real}\:{values}\:{of}\:{x}\:{for}\:{which} \\ $$$${the}\:{function}\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{2}} \\ $$$$ \\ $$
Commented by mrW1 last updated on 23/Apr/17
$${the}\:{question}\:{is}\:{not}\:{complete}! \\ $$
Commented by shardon last updated on 23/Apr/17
$${yes}\:{it}\:{does} \\ $$
Commented by mrW1 last updated on 23/Apr/17
$${what}\:{is}\:{your}\:{question}\:{then}? \\ $$
Answered by FilupS last updated on 24/Apr/17
$${f}\left({x}\right)=\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{2}} \\ $$$${x}\in\mathbb{R} \\ $$$$\: \\ $$$${x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{2}\neq\mathrm{0}\:\:\:\Rightarrow\:\:\:{x}\neq−\mathrm{2},\:−\mathrm{1} \\ $$$$\: \\ $$$$\forall{x}\in\mathbb{R}\backslash\left\{−\mathrm{2},\:−\mathrm{1}\right\}\Rightarrow{f}\in\mathbb{R} \\ $$