Question Number 86189 by oustmuchiya@gmail.com last updated on 27/Mar/20
$${Given}\:{that}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{7}}{\mathrm{8}}\:{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\:\frac{\mathrm{3}\boldsymbol{\mathrm{x}}−\mathrm{6}}{\mathrm{6}},\:{find} \\ $$$$\left(\mathrm{a}\right)\:\boldsymbol{\mathrm{g}}\left(\mathrm{6}\right),\:\left(\mathrm{b}\right)\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\:\:\:\left(\mathrm{c}\right)\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{\mathrm{x}}\:{if}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right) \\ $$
Answered by Kunal12588 last updated on 27/Mar/20
$$\left({a}\right)\:{g}\left(\mathrm{6}\right)=\frac{\mathrm{18}−\mathrm{6}}{\mathrm{6}}=\mathrm{2} \\ $$$$\left({b}\right)\:{f}^{−\mathrm{1}} \left({x}\right)=\frac{\mathrm{8}{x}−\mathrm{7}}{\mathrm{2}} \\ $$$$\left({c}\right)\:\mathrm{12}{x}+\mathrm{42}=\mathrm{24}{x}−\mathrm{48} \\ $$$$\Rightarrow\mathrm{12}{x}=\mathrm{90} \\ $$$$\Rightarrow{x}=\frac{\mathrm{15}}{\mathrm{2}}=\mathrm{7}.\mathrm{5} \\ $$