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f-2x-1-3x-2-x-1-x-2-faind-f-1-2-




Question Number 185665 by mathlove last updated on 25/Jan/23
f(((2x−1)/(3x+2)))=((x−1)/(x−2))      faind   f^(−1) (2)=?
$${f}\left(\frac{\mathrm{2}{x}−\mathrm{1}}{\mathrm{3}{x}+\mathrm{2}}\right)=\frac{{x}−\mathrm{1}}{{x}−\mathrm{2}}\:\:\:\:\:\:{faind}\:\:\:{f}^{−\mathrm{1}} \left(\mathrm{2}\right)=? \\ $$
Answered by cortano1 last updated on 25/Jan/23
f^(−1) (((x−1)/(x−2)))=((2x−1)/(3x+2))   ⇔ ((x−1)/(x−2)) = 2 ; x−1=2x−4  ⇔ x=3   ⇔f^(−1) (2)=((2.3−1)/(3.3+2))=(5/(11))
$${f}^{−\mathrm{1}} \left(\frac{{x}−\mathrm{1}}{{x}−\mathrm{2}}\right)=\frac{\mathrm{2}{x}−\mathrm{1}}{\mathrm{3}{x}+\mathrm{2}}\: \\ $$$$\Leftrightarrow\:\frac{{x}−\mathrm{1}}{{x}−\mathrm{2}}\:=\:\mathrm{2}\:;\:{x}−\mathrm{1}=\mathrm{2}{x}−\mathrm{4} \\ $$$$\Leftrightarrow\:{x}=\mathrm{3}\: \\ $$$$\Leftrightarrow{f}^{−\mathrm{1}} \left(\mathrm{2}\right)=\frac{\mathrm{2}.\mathrm{3}−\mathrm{1}}{\mathrm{3}.\mathrm{3}+\mathrm{2}}=\frac{\mathrm{5}}{\mathrm{11}} \\ $$

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