Question

Find
`f^-1 ( x ) when f ( x ) = (3x)/(x-2)`

Answer 1

`f^(-1)`(x) =
`(2x)/(x-3)`

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

y =
`(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 =
`(2y)/(y-3)`

change y to x for inverse function

`f^(-1)`(x) =
`(2x)/(x-3)`