Show there exists a function $f: \Bbb R \to \Bbb R$ such that $ f(x)^5+f(x)^4+f(x)^3+f(x)^2+6f(x)=x, $ for all $x \in \Bbb R$.
Using linear algebra, if the 'system' is invertible then such function exists.
I can't recall this theorem.
I'm not sure it is the right approach either.