速救!若f（x）满足关系f（x）+2f（-x）=3x,求f（x）若fx满足关系f（x）+2f（-x）=3x,求fx

速救!若f（x）满足关系f（x）+2f（-x）=3x,求f（x）若fx满足关系f（x）+2f（-x）=3x,求fx
速救!若f（x）满足关系f（x）+2f（-x）=3x,求f（x）
若fx满足关系f（x）+2f（-x）=3x,求fx

速救!若f（x）满足关系f（x）+2f（-x）=3x,求f（x）若fx满足关系f（x）+2f（-x）=3x,求fx
令x=-x代入f（x）+2f（-x）=3x得f（-x）+2f（x）=-3x与f（x）+2f（-x）=3x整理,消去f（-x）
3f（x）=-9x解得f（x）=-3x

f（x）为偶函数，则3f（x）=3x，则f（x）=x
f（x）为奇函数，则f（x）-2f（x）=3x，则f（x）=-3x

f（x）+2f（-x）=3x (1)
f(-x)+2f(x)=-3x (2)

(1)-2*(2)
得：-3f(x)=9x
所以
f(x)=-3x

∵f(x)+2f(-x)=3x①
∴f(-x)+2f(x)=-3x②
解由①②组成方程得
f(x)=-3x