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Question Number 85500 by oustmuchiya@gmail.com last updated on 22/Mar/20
$${The}\:{function}\:{of}\:\boldsymbol{\mathrm{f}}\:{and}\:\boldsymbol{\mathrm{g}}\:{are}\:{defined}\:{by}\:\boldsymbol{\mathrm{f}}:\boldsymbol{\mathrm{g}}\rightarrow\frac{{x}}{\boldsymbol{\mathrm{b}}{x}−\mathrm{2}},\:{x}\:\neq\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{b}}}\:{and}\:\boldsymbol{\mathrm{b}}\:\neq\:\mathrm{0},\:{where}\:\boldsymbol{\mathrm{a}}\:{and}\:\boldsymbol{\mathrm{b}}\:{are}\:{real}\:{numbers}\:\boldsymbol{\mathrm{g}}:\boldsymbol{\mathrm{x}}\:\rightarrow\mathrm{2}{x}−\mathrm{11} \\ $$$$\left({a}\right)\:{If}\:\boldsymbol{\mathrm{f}}\left(\mathrm{2}\right)=\:\frac{-\mathrm{1}}{\mathrm{2}}\:{and}\:\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\mathrm{1}\right)\:=\:-\mathrm{1},\:{find}\:\boldsymbol{\mathrm{a}}\:{and}\:\boldsymbol{\mathrm{b}}\:{and}\:{write}\:{down}\:{the}\:{expression}\:{for}\:\boldsymbol{\mathrm{f}}\:{in}\:{terms}\:{of}\:\boldsymbol{\mathrm{x}} \\ $$$$\left(\boldsymbol{\mathrm{b}}\right)\:\boldsymbol{\mathrm{F}}{ind}\:{the}\:{value}\:{of}\:\boldsymbol{\mathrm{x}}\:{for}\:{which}\:\boldsymbol{\mathrm{fg}}\left(\boldsymbol{\mathrm{x}}\right)=\:\frac{-\mathrm{1}}{\mathrm{2}} \\ $$
Answered by john santu last updated on 22/Mar/20
$${nothing}\:{a}\:{in}\:{your}\:{question} \\ $$