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已知f(x+1/x-1)=3f(x)-2x,求f(x)
人气:116 ℃ 时间:2020-10-01 18:28:27
解答
设t=(x+1)/(x-1)
则x=(t+1)/(t-1)
f(t)=3f(t+1/t-1)-2(t+1)/(t-1)
即f(x)=3f(x+1/x-1)-2(x+1)/(x-1)
联立原式,消去f(x+1/x-1)
f(x)=3x/4+(x+1)/4(x-1)
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