How can I eliminate arbitrary functions from Z=f (y+2x) +g (y-3x)?

Answer 1

I think we need a little more information here. You say eliminate the arbitrary functions f, and g? You could always take the partial derivative with respect to a third variable w, such that w is not a function of y or x. If you wish to change variables you could let u=y+2x, and v=y-3x. So that Z=f(u)+g(v).