Question

已知y=f(x)是定义在R上的函数,且对任意x属于R,有f(x+2)[1-f(x)]=f(x)+1成立（1）证明f(x)

Answer 1

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

f(x+4) = (1+f(x+2))/(1-f(x+2)) = -1/f(x);

f(x+8) = f(x);

所以f(x)是以8为周期的周期函数.

f(2002) = f(250*8 +2) = f(2) = 2;