Functional Equation: f(x)+f(x+1)=(f(x+2))/(x+1)

Bulkyd said:
Could anyone have a try with this?

f(x)+f(x+1)=(f(x+2))/(x+1)
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What were the instructions? What are you needing to do? What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please be complete, including class subject (real analysis? etc) and recent topics of study (such as the gamma function and the subfactorial function). Thank you! ;)
 
stapel said:
What were the instructions? What are you needing to do? What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please be complete, including class subject (real analysis? etc) and recent topics of study (such as the gamma function and the subfactorial function). Thank you! ;)
Click to expand...
Well the instructions were to find all possible R>R functions which satisfy the above equation. I don't really know how to approach this, so help would be appreciated.
 
Quite frankly, if those are the only instructions, I don't KNOW how to solve it. The equation is meaningless if x is minus 1 so how can it go from R, which quite obviously includes minus 1. The question does not even make sense to me.

I would probably start by trying a negative approach. What kinds of attributes must such a function NOT have. There are an infinite number of possible functions. Excluding large numbers of them strikes me as having some promise as a route to finding a solution.
 
Bulkyd said:
Well the instructions were to find all possible R>R functions which satisfy the above equation. I don't really know how to approach this, so help would be appreciated.
Click to expand...
What kind of class are you in? What tools and techniques have you studied recently? What did you think of the results at the link posted earlier? ;)
 
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