Question 10
(GRE 3) Let $g:\mathbb C\to\mathbb C$, $w\in\mathbb C$, $a\in\mathbb C$, $w^3=1$ $(w\ne1)$. Show that there is one and only one function $f:\mathbb C\to\mathbb C$ such that
$$f(z)+f(wz+a)=g(z),\qquad z\in\mathbb C.$$
Find the function $f$.
$$f(z)+f(wz+a)=g(z),\qquad z\in\mathbb C.$$
Find the function $f$.