设 f(x) = ax^2+bx+c
因为f(0)=0,所以 c = 0
f(x+1) = a(x+1)^2+b(x+1)
= ax^2+bx+2ax+a+b
= f(x) + 2ax + a+b
所以 2a=1 a=1/2
a+b = 1 b = 1/2
所以 f(x)=1/2(x)^2+1/2(x)
g(x) = 2f(-x)+x
=x^2
f(g(x))=f(x^2)=1/2(x)^4 + 1/2(x)^2
答案为
f(x)=1/2(x)^2+1/2(x)
f(g(x))=f(x^2)=1/2(x)^4 + 1/2(x)^2