Question

一道关于函数的周期性的数学题已知函数f(x)满足f(x+2)·[1-f(x)]=1+f(x)问：若f(x)=负根号3,求

Answer 1

f(x+2)-f(x+2)f(x)=1+f(x)

f(x+2)-1= f(x)[ f(x+2)+1]

f(x)= [f(x+2)-1]/ [ f(x+2)+1] (1)

f(x-2)= [f(x)-1]/ [ f(x)+1] (2)

将（1）f(x)中的代入（2）分子分母同乘[ f(x+2)+1]化简得

f(x-2) f(x+2)=-1

然后f(x-4) f(x)=-1

f(x) f(x+4)=-1

f(x-4) = f(x+4)

f(x) = f(x+8)

T=8

余下的你完成吧!