Question

已知函数f（x）满足2f（x）+3f（-x）=x2+x，则f（x）=______

已知函数f（x）满足2f（x）+3f（-x）=x2+x，则f（x）=______．

Answer 1

∵2f（x）+3f（-x）=x²+x，①
∴2f（-x）+3f（x）=x²-x，②

②×3?①×2

5

得：f（x）=

x2

5

?x
故答案为

x2

5

?x

Answer 2

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