Question

Find $f^-1 ( x ) when f ( x ) = \frac{3x}{x-2}$

Answer 1

$f^{-1}$(x) = $\frac{2x}{x-3}$

let y = f(x), then rearrange making x the subject

y = $\frac{3x}{x-2}$ ( 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 = $\frac{2y}{y-3}$

change y to x for inverse function

$f^{-1}$(x) = $\frac{2x}{x-3}$