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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-




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

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