已知二次函数f(x)满足f(0)=0,且f(x+1)=f(x)+x+1,g(x)=2f(-x)+x 求f(x)函数表达式 求f[g(x)]的表达式

设 f(x) = ax^2+bx+c因为f(0)=0,所以 c = 0f(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^2f(g(x))=f(x^2)=1/2(x)^4 + ...