已知f﹙x﹚满足2f﹙x﹚﹢f﹙x的倒数﹚=2x x属于实数 且x≠0 求f﹙x﹚

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已知f﹙x﹚满足2f﹙x﹚﹢f﹙x的倒数﹚=2xx属于实数且x≠0求f﹙x﹚已知f﹙x﹚满足2f﹙x﹚﹢f﹙x的倒数﹚=2xx属于实数且x≠0求f﹙x﹚已知f﹙x﹚满足2f﹙x﹚﹢f﹙x的倒数﹚=2x

已知f﹙x﹚满足2f﹙x﹚﹢f﹙x的倒数﹚=2x x属于实数 且x≠0 求f﹙x﹚
已知f﹙x﹚满足2f﹙x﹚﹢f﹙x的倒数﹚=2x x属于实数 且x≠0 求f﹙x﹚

已知f﹙x﹚满足2f﹙x﹚﹢f﹙x的倒数﹚=2x x属于实数 且x≠0 求f﹙x﹚
2f(x)+f(1/x)=2x (1)
令x=1/x
2f(1/x)+f(x)=2/x (2)
(1)×2-(2)
3f(x)=4x-2/x
f(x)=(4x²-2)/(3x)

2f(x) + f(1/x) = 2x (1)
put y=1/x
2f(1/y) + f(y) = 2/y
2f(1/x) + f(x) = 2/x (2)
2(1)-(2)
3f(x) = 4x - 2/x
f(x) = 2(2x^2-1)/ (3x)

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