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Question Number 86189 by oustmuchiya@gmail.com last updated on 27/Mar/20

Given that f(x)=((2x+7)/8) and g(x)= ((3x−6)/6), find  (a) g(6), (b)f^(−1) (x)   (c) the value of x if f(x)=g(x)

$${Given}\:{that}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{7}}{\mathrm{8}}\:{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\:\frac{\mathrm{3}\boldsymbol{\mathrm{x}}−\mathrm{6}}{\mathrm{6}},\:{find} \\ $$$$\left(\mathrm{a}\right)\:\boldsymbol{\mathrm{g}}\left(\mathrm{6}\right),\:\left(\mathrm{b}\right)\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\:\:\:\left(\mathrm{c}\right)\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{\mathrm{x}}\:{if}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right) \\ $$

Answered by Kunal12588 last updated on 27/Mar/20

(a) g(6)=((18−6)/6)=2  (b) f^(−1) (x)=((8x−7)/2)  (c) 12x+42=24x−48  ⇒12x=90  ⇒x=((15)/2)=7.5

$$\left({a}\right)\:{g}\left(\mathrm{6}\right)=\frac{\mathrm{18}−\mathrm{6}}{\mathrm{6}}=\mathrm{2} \\ $$$$\left({b}\right)\:{f}^{−\mathrm{1}} \left({x}\right)=\frac{\mathrm{8}{x}−\mathrm{7}}{\mathrm{2}} \\ $$$$\left({c}\right)\:\mathrm{12}{x}+\mathrm{42}=\mathrm{24}{x}−\mathrm{48} \\ $$$$\Rightarrow\mathrm{12}{x}=\mathrm{90} \\ $$$$\Rightarrow{x}=\frac{\mathrm{15}}{\mathrm{2}}=\mathrm{7}.\mathrm{5} \\ $$

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