Determine all functions f: R→R, such that:
f(f(x)) + x*f(x) = 1, for all x ∈ R.
Hmm. I thought that I posted, but it is not here.
Where I wound up was that I think the function might have some relation to the golden ratio.
If f(x) = x^y,
then f(f(x)) = x^(y^2) and x*f(x) = x^(y+1)
Since these need to be of the same order, then y^2 = y+1
y= (sqrt(5) +1)/2 = Phi (the Golden ration)
But this function does not work for most negative reals, so I am stuck.
I look forward to the solution.
Lost post