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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 $n(u,v)=\frac{u-v}{4}=n$.

EDIT So if this is what the question is about, then yes, one has to solve the system to get each of the variables in terms of the outputs of the two functions. This may be quite difficult for arbitrary pairs of functions, but in the linear case (as here) there is always Cramer's rule one can use, especially useful for large number of variables in linear systems.

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