Question

Just looking for any and all solutions of this functional equation...

Answer 1

\[f^n(x)=f(x)^n\]

To help clear up the notation:

\[f^3(x)=f(f(f(x)))\]
\[f(x)^3 = f(x)*f(x)*f(x)\]

Answer 2

1

Answer 3

hmm im trying to think about matrix transformations

Answer 4

is there a transformation where applying the matrix is like a unitary rotation

Answer 5

and then vector can also be unitary so multiplying by itself will leave it unitary

Answer 6

and there will be a solution wrt to some n