Hello !
I have a problem to solve this question :
Find all real continuous functions f verifing : f(x+1)=f(x)+f(1/x)
Have you ever seen this, could you help me please ?
Hello !
I have a problem to solve this question :
Find all real continuous functions f verifing : f(x+1)=f(x)+f(1/x)
Have you ever seen this, could you help me please ?
Can you tell us some of background to this equation,
its context etc?
RonL
Last edited by CaptainBlack; August 19th 2006 at 06:47 AM.
I would like but I don't know anything about this function except that it is continuous. Somebody ask me about such a function and I don't know where does it come from ...
I would like but I don't know anything about this function except that it is continuous. Somebody ask me about such a function and I don't know where does it come from ...
What makes it unusual that is a composition of, which usually are not solved for in functional equations.
Like PH said, this has a cyclical property to it and try replacing all x's with 1/x. The right side of the equation yields the same thing, showing that .