Question 932707
The idea is to replace f(x) with y, swap x and y, and then solve for y like so... 



{{{f(x)= (-2-5x)/(4 + 5x)}}}



{{{y= (-2-5x)/(4 + 5x)}}}



{{{x= (-2-5y)/(4 + 5y)}}}



{{{x(4 + 5y)= -2-5y}}}



{{{4x + 5xy= -2-5y}}}



{{{4x + 5xy+5y= -2}}}



{{{5xy+5y= -2-4x}}}



{{{5xy+5y= -4x-2}}}



{{{y(5x+5)= -4x-2}}}



{{{y= (-4x-2)/(5x+5)}}}



So the inverse is *[Tex \LARGE f^{-1}(x) = \frac{-4x-2}{5x+5}]


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