Question 5
Let $\mathbb R$ denote the real numbers. Find all functions $f:\mathbb R\to\mathbb R$ satisfying:
(i) only finitely many real $s$ satisfy $f(s)=0$;
(ii) $f(x^4+y)=x^3f(x)+f(f(y))$ for all real $x,y$.
(i) only finitely many real $s$ satisfy $f(s)=0$;
(ii) $f(x^4+y)=x^3f(x)+f(f(y))$ for all real $x,y$.