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Topic: a functional equation
Replies: 6   Last Post: Jun 18, 1996 6:21 PM

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Vijay Fafat

Posts: 3
Registered: 12/12/04
a functional equation
Posted: Jun 14, 1996 6:34 PM
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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?


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