1.已知等式f(x)+2f(1/x)=3x,求f(x) 2.设函数y=f(x)满足f(x)+2f(-x)=-x^2+2x

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1.已知等式f(x)+2f(1/x)=3x,求f(x) 2.设函数y=f(x)满足f(x)+2f(-x)=-x^2+2x,求函数y=f(x)

f(x)+2f(1/x)=3x,则将1/x代入得f(1/x)+2f(x)=3/x,可得f(x)=2/x-x\x0d\x0d
f(x)+2f(-x)=-x^2+2x,将-x代入得f(-x)+2f(x)=-x^2-2x,可得f(x)=(-x^2)/3-2x

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