高一数学：函数的奇偶性

f(x)=x^3+x
2[f（x1）+f（x2）+f（x3）]
=2[(x1)^3+x1+(x2)^3+x2+(x3)^3+x3]
=[(x1)^3+(x2)^3]+[(x2)^3+(x3)^3]+[(x3)^3+(x1)^3]
+[x1+x2]+[x2+x3]+[x3+x1]
={(x1+x2)[(x1)^2-x1x2+(x2)^2]}+
{(x2+x3)[(x2)^2-x2x3+(x3)^2]}+
{(x3+x1)[(x3)^2-x3x1+(x1)^2]}+
[x1+x2]+[x2+x3]+[x3+x1]
=(1/2){(x1+x2)[2(x1)^2-2x1x2+2(x2)^2]}+
(1/2){(x2+x3)[2(x2)^2-2x2x3+2(x3)^2]}+
(1/2){(x3+x1)[2(x3)^2-2x3x1+2(x1)^2]}+
[x1+x2]+[x2+x3]+[x3+x1]
=(1/2){(x1+x2)[(x1-x2)^2+(x1)^2+(x2)^2]}+
(1/2){(x2+x3)[(x2-x3)^2+(x2)^2+(x3)^2]}+
(1/2){(x3+x1)[(x3-x1)^2+(x3)^2+(x1)^2]}+
[x1+x2]+[x2+x3]+[x3+x1]
>=(1/2){0*[0+0+0]}+
(1/2){0*[0+0+0]}+
(1/2){0*[0+0+0]}+
0+0+0=0