设f(x)+2f(1/x)=x,求f(x)

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设f(x)+2f(1/x)=x,求f(x)
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设f(x)+2f(1/x)=x,求f(x)
设f(x)+2f(1/x)=x,求f(x)

设f(x)+2f(1/x)=x,求f(x)
f(x) + 2f(1/x) = x (1)
f(1/x) + 2f(x) = 1/x
2f(1/x) + 4f(x) = 2/x (2)
(2) - (1)
3f(x) = 2/x - x
f(x) = (2-x^2)/(3x) (x不等于0)