Question

How do you find the inverse of `f(x) = (2x-1)/(x-1)`?

Answer 1

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

Explanation:

let `f_x` = `y`
`x=f^-1y`
`y` = `(2x-1)/(x-1)`

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

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

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

`-1/x`=`1/(y-1)-1`
`x=(y-1)/(y-2)`
`f^-1y`= `(y-1)/(y-2)`
replacing y with x
`f^-1(x)`= `(x-1)/(x-2)`