Question 1
Let $\mathbb{R}$ denote the set of all real numbers. Find all functions $f$ from $\mathbb{R}$ to $\mathbb{R}$ satisfying:
(i) there are only finitely many $s$ in $\mathbb{R}$ such that $f(s)=0$, and
(ii) $f\left(x^{4}+y\right)=x^{3} f(x)+f(f(y))$ for all $x, y$ in $\mathbb{R}$.
(i) there are only finitely many $s$ in $\mathbb{R}$ such that $f(s)=0$, and
(ii) $f\left(x^{4}+y\right)=x^{3} f(x)+f(f(y))$ for all $x, y$ in $\mathbb{R}$.