[tex]f^{-1}[/tex](x) = [tex]\frac{2x}{x-3}[/tex]
let y = f(x), then rearrange making x the subject
y = [tex]\frac{3x}{x-2}[/tex] ( multiply both sides by (x - 2 ))
y(x - 2 ) = 3x (distribute )
xy - 2y = 3x ( subtract 3x and add 2y to both sides )
xy - 3x = 2y (factor out x on left side )
x(y - 3 ) = 2y ( divide both sides by (y - 3) )
x = [tex]\frac{2y}{y-3}[/tex]
change y to x for inverse function
[tex]f^{-1}[/tex](x) = [tex]\frac{2x}{x-3}[/tex]
