Question

已知函数f(x)满足2f(x)+3f(-x)=x^2+x,则f(x)=?

Answer 1

由2f(x)+3f(-x)=x^2+x得2f(-x)+3f(x)=x^2-x，两个方程联立可求得f(x)=0.2x^2-x

Answer 2

2f(x)+3f(-x)=x^2+x
则2f(-x)+3f(x)=x^2-x
于是
4f(x)+6f(-x)=2x^2+2x
6f(-x)+9f(x)=3x^2-3x
解得：f(x)=(1/5)x^2-x

Answer 3

函数方程的题目
2f(x)+3f(-x)=x^2+x （1）
将x换成-x
2f(-x)+3f(x)=x^2-x (2)
(1)*2-(2)*3
-5f(x)=-x^2+5x
f(x)=x^2/5 -x

Answer 4

将-x代入等式，
2f(-x)+3f(x)=x^2-x

6f(-x)+9f(x)=3*x^2-3x
4f(x)+6f(-x)=2*x^2+2x
所以5f(x)=x^2-5x
得f(x)=1/5*x^2-x

Answer 5

2f(x)+3f(-x)=x^2+x
2f(-x)+3f(x)=x^2-x

4f(x)+6f(-x)=2x^2+2x
6f(-x)+9f(x)=3x^2-3x
相减5f(x)=x^2-5x
f(x)=1/5x^2-x