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[函数] 求$F(x)$

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isee posted 2014-9-4 08:56 |Read mode

对所有实数$x$，确定满足下列函数方程的函数$F(x)$:\[x^2F(x)+F(1-x)=2x-x^4.\]

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realnumber posted 2014-9-4 09:21

常规就x用1-x替换，解关于f(x),f(1-x)的方程组，难道有陷阱？

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爪机专用 posted 2014-9-4 09:33

回复 2# realnumber

没看出什么陷井

I am majia of kuing

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original poster isee posted 2014-9-4 13:39

回复 3# 爪机专用

没，只是题型总结，具有代表性与启发性

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