Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 24744 by NECx last updated on 25/Nov/17

If a function f is defined such that  f:R→R.If       f(x)=((3x−2)/(x^2 +5x−6)).Find the   (i)domain of f(x)  (ii)range of f(x)

$${If}\:{a}\:{function}\:{f}\:{is}\:{defined}\:{such}\:{that} \\ $$$${f}:\mathbb{R}\rightarrow\mathbb{R}.{If}\: \\ $$$$\:\:\:\:{f}\left({x}\right)=\frac{\mathrm{3}{x}−\mathrm{2}}{{x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{6}}.{Find}\:{the}\: \\ $$$$\left({i}\right){domain}\:{of}\:{f}\left({x}\right) \\ $$$$\left({ii}\right){range}\:{of}\:{f}\left({x}\right) \\ $$

Answered by ajfour last updated on 25/Nov/17

f(x)=((3(x−(2/3)))/((x+6)(x−1)))  ⇒ x∈ (−∞, −6)∪(−6, 1)∪(1, ∞)  Range ∈ (−∞, ∞) .

$${f}\left({x}\right)=\frac{\mathrm{3}\left({x}−\frac{\mathrm{2}}{\mathrm{3}}\right)}{\left({x}+\mathrm{6}\right)\left({x}−\mathrm{1}\right)} \\ $$$$\Rightarrow\:{x}\in\:\left(−\infty,\:−\mathrm{6}\right)\cup\left(−\mathrm{6},\:\mathrm{1}\right)\cup\left(\mathrm{1},\:\infty\right) \\ $$$${Range}\:\in\:\left(−\infty,\:\infty\right)\:. \\ $$

Commented by NECx last updated on 25/Nov/17

thanks boss

$${thanks}\:{boss} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com