Question

F(x) = 2x+1/×-1 find the inverse function

Answer 1

To factor this, start by replacing x with y and then solve for y

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

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

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

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

`xy -x = 2y+1`

`xy - 2y -x +x = 2y - 2y +x+1`

`xy - 2y = x+1`
Factor out y on the left side.

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

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

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

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

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