Question

f(x+y)=f(x)+f(y)/1-f(x)f(y)

求满足方程f(x+y)=f(x)+f(y)/1-f(x)f(y)的函数f(x),其中已知f'(0)存在.

Answer 1

简单计算一下即可，答案如图所示

Answer 2

令x=y=0带入得
f(0)=2f(0)/(1-f(0)^2)
求得f(0)=0
令y=-x带入得
f(0)=[f(x)+f(-x)] / [1-f(x)f(-x)]=0
即f(x)=-f(-x)