Question Number 24744 by NECx last updated on 25/Nov/17
$${If}\:{a}\:{function}\:{f}\:{is}\:{defined}\:{such}\:{that} \\ $$$${f}:\mathbb{R}\rightarrow\mathbb{R}.{If}\: \\ $$$$\:\:\:\:{f}\left({x}\right)=\frac{\mathrm{3}{x}−\mathrm{2}}{{x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{6}}.{Find}\:{the}\: \\ $$$$\left({i}\right){domain}\:{of}\:{f}\left({x}\right) \\ $$$$\left({ii}\right){range}\:{of}\:{f}\left({x}\right) \\ $$
Answered by ajfour last updated on 25/Nov/17
$${f}\left({x}\right)=\frac{\mathrm{3}\left({x}−\frac{\mathrm{2}}{\mathrm{3}}\right)}{\left({x}+\mathrm{6}\right)\left({x}−\mathrm{1}\right)} \\ $$$$\Rightarrow\:{x}\in\:\left(−\infty,\:−\mathrm{6}\right)\cup\left(−\mathrm{6},\:\mathrm{1}\right)\cup\left(\mathrm{1},\:\infty\right) \\ $$$${Range}\:\in\:\left(−\infty,\:\infty\right)\:. \\ $$
Commented by NECx last updated on 25/Nov/17
$${thanks}\:{boss} \\ $$