f(x)=f1(x)=(x-1)/(x+1),fn+1=f[fn(x)],这个函数周期4,求f2,f3,f4推导过程,

问题描述:

f(x)=f1(x)=(x-1)/(x+1),fn+1=f[fn(x)],这个函数周期4,求f2,f3,f4推导过程,

易知 f2=f[f1(x)]-1=-1/x-1
f3=f[f2(x)]-1=(f2-1)/(f2+1) -1=2*x
f4=f[f3(x)]-1=(f3-1)/(f3+1) -1=-2/(2*x+1)
f5=f[f4(x)]-1=(f4-1)/(f4+1) -1=(x-1)/(x+1)=f1
所以周期是4