
a functional equation
Posted:
Jun 14, 1996 6:34 PM


I have the following functional equation:
f(x+g(x))  f(x) = constant.
I've been able to find the following solutions by trial and guess:
f(x) = exp(x), g(x) = log(1+aexp(x))
f(x) = log(x), g(x) = ax
f(x) = x, g(x) = constant. f(x) = exp(x), g(x) = log(1+aexp(x)).
I'd like to know if there are any other solutions. In general, is there any systematic way of attacking these problems?
vijay

