Find the inverse function

[Skizye]

Homework Statement

If $$F(x) = \frac{x}{x + 1}$$, then the inverse function, $$f^{-1}$$, is given by $$f^{-1}(x) =$$

Homework Equations

The Attempt at a Solution

I've replaced F(x) with y, and switched the x and y variables. Where I'm having a problem is solving the resulting equation, here's what I've done so far.

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

$$xy + x = y$$,

$$x(y + 1) = y$$,

but as far as I can tell that just takes me back to where I started.

Also, I believe this is a question from an old AP Calculus exam. It's technically homework from a calculus class but seems to primarily involve algebra. Did I put it in the right forum or should it have gone in the precalculus forum? Thanks!

 

[statdad]

Go back to $xy + x = y$, gather the $y$ values together, then solve.

 

[micromass]

When you reach the equation xy+x=y. Try to solve for y... That is, separate the y from the x...