Question

How do you find `f ^-1(x)` given `f(x) = (x+1)/(x+2)` when x ≠ -2?

Answer 1

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

Explanation:

First : we will replace all `x` by `y` and the `y` by `x`

Here we have :
`x=(y+1)/(y+2)`

Second: solve for `y`

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

Arrange all `y` in one side:

`x*y - y= 1-2*x`

Taking `y` as common factor we have:
`y*(x-1)=1-2*x`
`y=(1-2*x)/(x-1)`

Therefore,
`f^-1(x)=(1-2*x)/(x-1)`