n0ya
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I have a 2D function f:
f(x,y) = a + bx + cy + dxy
what is the inverse of this function?
f(x,y) = a + bx + cy + dxy
what is the inverse of this function?
What is the Inverse of a 2D Function?
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Hi n0ya! 
The function you mention will never have an inverse.
For example, if f(x,y)=2+x, then f cannot have an inverse since f(0,0)=2=f(0,1). Thus (0,0) and (0,1) are both being sent to 2. But then the inverse needs to send 2 to both (0,0) and (0,1), but this is impossible for a function.
In general, your function is one [itex]f:\mathbb{R}^2\rightarrow \mathbb{R}[/itex], it can have no (continuous) inverse since otherwise the plane would be homeomorphic to the line. And this cannot be.
If you had a function [itex]f:\mathbb{R}^2\rightarrow \mathbb{R}^2[/itex] then you might have a continuous inverse. But even then this depends of the function f...
The function you mention will never have an inverse.
For example, if f(x,y)=2+x, then f cannot have an inverse since f(0,0)=2=f(0,1). Thus (0,0) and (0,1) are both being sent to 2. But then the inverse needs to send 2 to both (0,0) and (0,1), but this is impossible for a function.
In general, your function is one [itex]f:\mathbb{R}^2\rightarrow \mathbb{R}[/itex], it can have no (continuous) inverse since otherwise the plane would be homeomorphic to the line. And this cannot be.
If you had a function [itex]f:\mathbb{R}^2\rightarrow \mathbb{R}^2[/itex] then you might have a continuous inverse. But even then this depends of the function f...
n0ya
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Thanks!