f（1-x/1+x）=1-x²/1+x²,求f（x）中带入后(1+y)^2-(1-y)^2)/((1+y)^2+(1-y)^2)这步怎么带入的求解释设y=1-x/1+xx=1-y/1+y=>1-xx/1+xx=((1+y)^2-(1-y)^2)/((1+y)^2+(1-y)^2)=2y/(1+y^2)=>f(x)=2x/(1+xx)

Question

f（1-x/1+x）=1-x²/1+x²,求f（x）中带入后(1+y)^2-(1-y)^2)/((1+y)^2+(1-y)^2)这步怎么带入的求解释
设 y = 1-x/1+x
x = 1-y/1+y
=>
1-xx/1+xx = ((1+y)^2-(1-y)^2)/((1+y)^2+(1-y)^2) = 2y/(1+y^2)
=>
f(x)=2x/(1+xx)

Answer 1

你这个问题补充都已经写出过程来了啊.
在原式f（1-x/1+x）=1-x²/1+x²中令1-x/1+x=y,可以求得x = 1-y/1+y
把x = 1-y/1+y带入1-xx/1+xx就得到了f（y）=2y/(1+y^2),把y换成x就得到了f（x）.