riley1012 riley1012

08-08-2017
Mathematics

contestada

Find the inverse

f(x) = [tex] \frac{x}{x + 2} [/tex]

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jdoe0001 jdoe0001

08-08-2017

[tex]\bf f(x)=y=\cfrac{x}{x+2}\impliedby \textit{let's switch the variables} \\\\\\ \boxed{x}=\cfrac{\boxed{y}}{\boxed{y}+2}\implies x(y+2)=y\implies xy+2x=y \\\\\\ xy-y=2x\implies y(x-1)=2x\implies y=\cfrac{2x}{x-1}\impliedby f^{-1}(x)[/tex]

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