Question

What is the inverse function of the picture given

Answer 1

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

Explanation:

let y = f(x)

then y =
`(x)/(x-2)`

rearrange making x the subject, cross- multiply

y(x - 2) = x

xy - 2y = x ( subtract x from both sides )

xy - x - 2y = 0 ( add 2y to both sides )

xy - x = 2y ( factor out x from each term on the left side )

x(y - 1) = 2y ( divide both sides by (y - 1)

x =
`(2y)/(y-1)`

change y back into terms of x

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