Inverse of F(x)= x/(x+1): How to Find the Inverse Function | Step-by-Step Guide

[Squeezebox]

1. The problem

Find the inverse of F(x)= x/(x+1)

The Attempt at a Solution

I have no idea where to begin. Everything I have tried has just taken me back to the original equation.

 

[Defennder]

There is a technique for finding an inverse of a function f(x), if it exists. Let y = f(x). Express x in terms of y to get x = g(y). Replace y with x and there's your inverse function.

 

[statdad]

This is similar to, but slightly more direct than, the method in the previous post.

Start with your function.

$$y = \frac x {x+1}$$

Interchange the variables.

$$x = \frac y {y+1}$$

Solve the second equation for $$y$$ in terms of $$x$$ - the result is the inverse function.