I have managed to guess one solution of this function : $f(x)=1-x^{3}$, but I have no idea how to prove it unique, or get other solutions.
If this is not solvable, how can you prove this function have negative derivative at interval $(0,1)$?
2026-04-06 03:19:39.1775445579
How to solve this functional equation: $f(1-f(x))=1-x^{9}, f(1)=0$
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A hint:
Consider the function $g(x):=1-f(x)$.