Let f,g, and h be some functions and x and y be scalar variables. The functions are related in the following way:
f(x) + g(y) = h(x-y)
The question is: can functions f, g, and h be anything besides linear functions (f(x)=a*x+b, g(y)=-a*y+c, h(x)=a*x+b+c)? In other words, is there another solution to the functional equation besides the linear one?
Konstantin K. Avilov
George, thanks a lot! Your answer appears to be conclusive despite you have not specified explicitly that for "non-pathological" functions f, g, and h the only solution is the linear one.
https://en.wikipedia.org/wiki/Cauchy%27s_functional_equation
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