f(x+2)=[1+f(x)]/[1-f(x)]
∴f(x+4)=f(x+2+2)=[1+f(x+2)]/[1-f(x+2)]={1+[1+f(x)]/[1-f(x)]}/{1-[1+f(x)]/[1-f(x)]}
=[1-f(x)+1+f(x)]/[1-f(x)-1-f(x)]=2/[-2f(x)]=-1/f(x)∴f(x+8)=f(x+4+4)
=-1/f(x+4)=-1/[-1/f(x)]=f(x),即f(x)是周期为8的函数
f(x+2)=[1+f(x)]/[1-f(x)]
∴f(x+4)=f(x+2+2)=[1+f(x+2)]/[1-f(x+2)]={1+[1+f(x)]/[1-f(x)]}/{1-[1+f(x)]/[1-f(x)]}
=[1-f(x)+1+f(x)]/[1-f(x)-1-f(x)]=2/[-2f(x)]=-1/f(x)∴f(x+8)=f(x+4+4)
=-1/f(x+4)=-1/[-1/f(x)]=f(x),即f(x)是周期为8的函数