Question

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

Answer 1

Let `y = f(x)` and solve for `x` in terms of `y` to find:

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

Explanation:

Let `y = f(x) = (x-2)/(x+2) = ((x+2)-4)/(x+2) = 1-4/(x+2)`

Then `1-y = 4/(x+2)`

Hence `x+2 = 4/(1-y)`

So `x = 4/(1-y)-2 = (4-2(1-y))/(1-y) = (2y+2)/(1-y) = (2(y+1))/(1-y)`

So `f^(-1)(y) = (2(y+1))/(1-y)`