Question 192120
{{{f(x) = (5x-3)/(x-2)}}} Start with the given function. The domain here is that "x" can be any real number except {{{x<>2}}}



{{{y = (5x-3)/(x-2)}}} Replace f(x) with y



{{{x = (5y-3)/(y-2)}}} Swap x and y



{{{x(y-2) = 5y-3}}} Multiply both sides by y-2



{{{xy-2x = 5y-3}}} Distribute



{{{xy=5y-3+2x}}} Add {{{2x}}} to both sides.



{{{xy-5y=-3+2x}}} Subtract {{{5y}}} from both sides.



{{{xy-5y=2x-3}}} Rearrange the terms.



{{{y(x-5)=2x-3}}} Factor out the GCF "y"



{{{y=(2x-3)/(x-5)}}} Divide both sides by x-5




So the inverse function is *[Tex \LARGE f^{-1}(x)=\frac{2x-3}{x-5}]. The domain here is that "x" can be any real number except {{{x<>5}}}