求证明；f(X)=f(x+1)+f(x-1)是周期函数
问题描述：
求证明；f(X)=f(x+1)+f(x-1)是周期函数
答
f(x + 1) = f(x) - f(x - 1)f(x + 2) = f(x + 1) - f(x) = f(x) - f(x - 1) - f(x) = -f(x - 1)f(x + 3) = f(x + 2) - f(x + 1) = -f(x - 1) - f(x) + f(x - 1) = -f(x)f(x + 6) = f(x + 3 + 3) = -f(x + 3) = f(x)...谢谢你的回答，但是为什么；f(x + 6) = f(x + 3 + 3) = -f(x + 3) = f(x)把 x + 6 看成 x + 3 + 3然后根据f(x + 3) = -f(x)把 x 的地方用 x + 3 整体来代替，就可以得到 f(x + 3 + 3) = -f(x + 3) 又因为 -f(x + 3) = - [-f(x)] = f(x)所以 f(x + 3 + 3) = f(x)即 f(x + 6) = f(x)