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
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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