Inverse function of a two variable function

[misterau]

Homework Statement

I'm wondering how to find the inverse function of some f(x,y)?

Homework Equations

The Attempt at a Solution

 

[Ray Vickson]

Homework Statement

I wondering how to find the inverse function of some f(x,y)?

Homework Equations

The Attempt at a Solution

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.

 

[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

 

[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.

 

[Redbelly98]

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.