Judging from the numeric approximation, neither of those seem to be the case. I will try it and see what happens though.
I have tried many things. One thing I was considering was to use the cross correlation of f(x) with a conveniently chosen function, make a substitution, and use the...
Ok, so I can make a substitution:
y(x) = x + 1 + f(-x). Then
y ' (x) = 1 - f ' (-x).
I don't see where to go from there, since y ' (x) does not appear in the original equation. However
y ' (-x) = 1 - f ' (x) does appear in the original equation. If i make that substitution I get...
I am trying to solve:
(x + 1 + f(-x) )(1 - f ' (x) ) = x+1
f(0) = x_0
x in (-1,1)
I approximated it numerically but any analytic method I try fails. Any ideas?