# How do you find the inverse of a function that has 2 equations

It's the same thing as when we have 1 equation, but we need to solve the system of equations?

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Couly you please give an example? –  MJD Nov 6 '12 at 23:18
I can't think of one. Sorry. –  George Milton Nov 6 '12 at 23:19
If you don't know of a single example of a function that has two equations, why do you care how to find the inverse of one? –  MJD Nov 6 '12 at 23:27
g(m,n) = m+2n and m-2n –  George Milton Nov 6 '12 at 23:27
it's a matrix function i guess –  George Milton Nov 6 '12 at 23:53

In one of Milton's responses above, the example of the two functions $m+2n$ and $m-2n$ is mentioned. If these are to be viewed as two functions in the two unknowns $m,n$ then one can define $u(m,n)=m+2n$ and $v(m,n)=m-2n$. Then $\frac{u-v}{4}=n$, while $\frac{u+v}{2}=m$. So one can say that the inverse functions are $m(u,v)=\frac{u+v}{2}$ and $n(u,v)=\frac{u-v}{4}=n$.