need help regarding superposition principle..!!
if we have a function f(x)=y that takes one and only one input and now we will consider two inputs x1,x2
we state superposition principle as function is linear if f(x1+x2)=f(x1+x2)
please correct me if i am wrong upto here..!
now my problem is that what happens if we take three variables one dependent and two independent as in function z=g(x,y) [please note here i have taken x,y as independent functions while in previous case i have considered only x as independent variable]
now if we have to prove that function z is linear then can we justify by this ( considering superposition principle as major factor) :
g(x1+x2,y1+y2)=g(x1,y1)+g(x2,y2)..?
if not then how can we prove superposition principle/linearity in function involving more than two variables...!!

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