# Inverse function of a two variable function

1. Aug 16, 2013

### misterau

1. The problem statement, all variables and given/known data
I'm wondering how to find the inverse function of some f(x,y)?

2. Relevant equations

3. The attempt at a solution

Last edited: Aug 17, 2013
2. Aug 17, 2013

### Ray Vickson

You need to define the question better. Do you want the curve of (x,y) values that give f(x,y) = c for some given c, or what? Typically, there will be many points, or no points, that give f(x,y) = c.

3. Aug 17, 2013

### misterau

I need to show that f(x,y) = x/y has a right inverse that is a function f-1: R → R2 \ { (x,0) |x ∈ R} so that f . f-1(x) = x

4. Aug 17, 2013

### HallsofIvy

The first, obvious, thing you will have to do is treat the sets {(x, y)|y> 0} and {(x, y)| y< 0} separately. For a given x, you want $(u,v)= f^{-1}(u)$ such that u/v= x. Even requiring that v be positive, there area an infinite number of such pairs. The point is that your function, f, maps an entire plane onto the line (x, 0). The inverse function has to map that line onto the plane. No function can do that.

5. Aug 18, 2013

### Redbelly98

Staff Emeritus
If the question as posted does not have an answer, let's let the OP, misterau, provide some clarification or correction.

misterau, please post the question in its exact words.