[จูกัดเหลียง]

2.Let the given equation be $e_0$ we clear that $f(x)+f(-x)=0$ get $f(0)=0$ and let $s_i\in\mathbb{R}$ such that $f(s_i)=0$ for any $i=1,2...n$
Let $\mathbb{S}=\left\{\,s_1,s_2...s_n\right\} $ have $n$ elements
put $x=0$ we have $f(x)=f(f(x))...(e_1)$
put $x=s_i,y=0$ get $f(s_i^4)=0$ but $S$ is the finite set so
$$\left\{\,s_1,s_2...s_n\right\} =\left\{\,-s_1,-s_2,..-s_n\right\} =\left\{\,s_i^4,s_2^4..s_n^4\right\} $$
so for any $x\in \mathbb{S}$ then $x\ge 0$ so $s_i=0$ for all $i$ then it's have only $0$ such that $f(0)=0$
so We find $f(x^4)=x^3f(x)...e_2$
from $e_1$ consider $$f(x^4+f(y))=x^3f(x)+f(y)=f(x^4+y)...e_3$$
put $y=-x^4$ in $e_3$ so $f(x^4-f(x^4))=f(x^4+f(-x^4))=0$ so $x^4=f(x^4)=x^3f(x)$
from $e_2$ so $f(x)=x$