Question 198369
{{{f(x)=(x-7)/(4x+8)}}} Start with the given function.



{{{y=(x-7)/(4x+8)}}} Replace f(x) with y



{{{x=(y-7)/(4y+8)}}} Switch each x with y (and vice versa). The goal now is to solve for y



{{{x(4y+8)=y-7}}} Multiply both sides by {{{4y+8}}}.



{{{4xy+8x=y-7}}} Distribute



{{{4xy=y-7-8x}}} Subtract 8x from both sides.



{{{4xy-y=-7-8x}}} Subtract y from both sides.



{{{4xy-y=-8x-7}}} Rearrange the terms.


 
{{{y(4x-1)=-8x-7}}} Factor out the GCF 'y'



{{{y=(-8x-7)/(4x-1)}}} Divide both sides by {{{4x-1}}}.



So the inverse is *[Tex \LARGE f^{-1}(x)=\frac{-8x-7}{4x-1}]