1. ## Inverse function

The problem is to find the inverse function of f expressed as f^-1(x).
f(x)=x/(1+x).
When i start to work on the problem i get stuck at
x=f(y)=y/(1+y)
x(1+y)=y
And i dont see a way to get it to f-1(x).
Somehow it should be f^-1(x)=x/(1-x).

Thankful for any help.

2. We have:

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

Solving:

$x=\dfrac{y}{1-y}=f^{-1}(y)$

Changing the name for the variable $y$:

$f^{-1}(x)=\dfrac{x}{1-x}$

Fernando Revilla

3. How did you get to $x=\dfrac{y}{1-y}$?

All I can get is $x=y(1+x)$

4. When finding the inverse, replace the x's with y's and y's with x's and then isolate the y.

$\displaystyle y=\frac{x}{1+x}\Rightarrow x=\frac{y}{1+y}\Rightarrow x(1+y)=y\Rightarrow x=y-xy\Rightarrow x=y(1-x)\Rightarrow f^{-1}(x)=\frac{x}{1-x}$