Question

How do you find the inverse of `y = (x+3)/(x-2)` and is it a function?

Answer 1

Inverse of `y=(x+3)/(x-2)` is `y=(2x+3)/(x-1)`

Explanation:

As `y=(x+3)/(x-2)`

`xy-2y=x+3`

or `xy-x=2y+3`

or `x(y-1)=2y+3`

or `x=(2y+3)/(y-1)`

Hence inverse of `y=(x+3)/(x-2)` is `y=(2x+3)/(x-1)`

Observe that each of the function is a reflection of the other in the line `x=y`.

graph{(y-(x+3)/(x-2))(y-(2x+3)/(x-1))(x-y)=0 [-10, 10, -5, 5]}