Question 998599
f(x)=(2x)/(x-3)



y=(2x)/(x-3) ... replace f(x) with y



x=(2y)/(y-3) ... swap x and y; now solve for y



x(y-3)=2y ... Multiply both sides by y-3.



xy-3x=2y ... Distribute



xy=2y+3x ... Add 3x to both sides.



xy-2y=3x ... Subtract 2y from both sides.



y(x-2)=3x ... Factor



y=3x/(x-2) ... Divide both sides by x-2.



The inverse function is *[Tex \LARGE f^{-1}(x) = \frac{3x}{x-2}]