UC知道f(1+1/x)=X/1-X的平方 求f(X)
来源：百度知道 编辑：UC知道 时间：2024/05/10 14:08:33
f((x+1)/x) = x/（1-x^2）
设(x+1)/x=t
x+1=tx
x=1/(t-1)
f(t)= 1/(t-1)/(1-1/(t-1)^2)
= 1/(t-1)/((t-1)^2-1)*(t-1)^2
=(t-1)/((t-1)^2-1)
=(t-1)/(t*(t-2))
f(x) =(x-1)/(x*(x-2))
设T=1+1/x
所以f(1+1/x)=f(T)
x=1/(T-1)
所以f(T)=[1/(T-1)]/[1-(1/(T-1))]
解得f(T)=1/(T-2)
将T用x带换
得f(x)=1/(x-2)
保对
f((x+1)/x) = (x/1-x)^2
设(x+1)/x=t 则
x=1/(t-1)
f(t)= [1/(t-1)/(1-1/(t-1))]^2
= (1/(t-2))^2
f(x) = [1/(x-2)]^2
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