\[ f( x,y) + g(x,y) \geq 6 \text{ and } f(x,y) \geq 2. \]

Jean can show that \(f\) and \(g\) are 2 functions on 2 variables \(x\) and \(y\) that satisfy the conditions above.

Given only that information, are you able to deduce the largest \(N\) such that \( g(x,y) \geq N \) for all real values of \(x\) and \(y\)?

If you think that no answer exists, enter in -1000.

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