need help regarding superposition principle..!!
hello everyone..
if we have a function y=f(x) then in-order to prove linearity we try to justify according to superposition principle as :
let x1 and x2 be two inputs then f(x1+x2)=f(x1)+f(x2)
please correct me if i am wrong upto here..
now what if we have more than two variables..let's say we have three variables two independent and one dependent
now we have function z=g(x,y)..now in-order to prove linearity for function involving more than two variables can i say this that for g(x,y) to be linear g(x1+x2,y1+y2)=g(x1,y1)+g(x2,y2)..??
and if this isn't the correct way for proving linearity in functions involving more than two variables..then please justify the correct method along with examples.

Question

need help regarding superposition principle..!!
hello everyone..
if we have a function y=f(x) then in-order to prove linearity we try to justify according to superposition principle as :
let x1 and x2 be two inputs then f(x1+x2)=f(x1)+f(x2)
please correct me if i am wrong upto here..
now what if we have more than two variables..let's say we have three variables two independent and one dependent 
now we have function z=g(x,y)..now in-order to prove linearity for function involving more than two variables can i say this that for g(x,y) to be linear g(x1+x2,y1+y2)=g(x1,y1)+g(x2,y2)..??
and if this isn't the correct way for proving linearity in functions involving more than two variables..then please justify the correct method along with examples.

shivaniits · Answer

@rajathsbhat @ganeshie8 ..can u please help me on this..!!