Question Number 86129 by oustmuchiya@gmail.com last updated on 27/Mar/20
$${Given}\:{that}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{8}\boldsymbol{\mathrm{x}}\:{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\mathrm{3}\boldsymbol{\mathrm{x}}−\mathrm{2}}{\mathrm{4}},\:{find} \\ $$$$\left(\mathrm{a}\right)\:\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\:\:\:\left(\mathrm{b}\right)\:{an}\:{expression}\:{for}\:\boldsymbol{{fg}}\left(\boldsymbol{\mathrm{x}}\right) \\ $$$$\left(\mathrm{c}\right)\:{value}\:{of}\:\boldsymbol{\mathrm{x}}\:{which}\:\boldsymbol{\mathrm{fg}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{20}\: \\ $$
Commented by jagoll last updated on 27/Mar/20
$$\left.\mathrm{a}\right)\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}}{\mathrm{8}} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{f}\left(\mathrm{g}\left(\mathrm{x}\right)\right)\:=\:\mathrm{8}\left(\frac{\mathrm{3x}−\mathrm{2}}{\mathrm{4}}\right)\:=\:\mathrm{6x}−\mathrm{4} \\ $$$$\left.\mathrm{c}\right)\:\mathrm{f}\left(\mathrm{g}\left(\mathrm{x}\right)\right)\:=\:\mathrm{6x}−\mathrm{4}\:=\:\mathrm{20} \\ $$$$\mathrm{x}\:=\:\frac{\mathrm{24}}{\mathrm{6}}\:=\:\mathrm{4} \\ $$