Question

How do you find the inverse of `f(x)= (2x+1)/(x-3)`?

Answer 1

`f^-1(x)=(1+3x)/(x-2)`

Explanation:

An inverse graph is found by reflecting the original graph in the line y=x. The easiest way to find the inverse function is by setting y=f(x), making x the subject and then switching y and x.

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

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

`xy-3y=2x+1`

`xy-2x=1+3y`

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

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

Therefore `f^-1(x)=(1+3x)/(x-2)`