f(x+1)=g(x)

f（x）= f(-x)
所f(x) = g(x - 1) = -g(1 - x) = - f(2 - x) = -f(x -2)
即是f(x) = - f(x - 2)
f(x - 2) = -f(x - 4)
所以f(x) = f(x - 4)
所以T =4

f（x）= f(-x)

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

f(x) = - f(x - 2)
f(x - 2) = -f(x - 4)

f(x) = f(x - 4)

T =4

对任意x0，g(x0)=-g(-x0)=-f(-x0+1)=-f(x0-1)=-g(x0-2)=g(2-x0)=f(3-x0)=f(x0-3)=g(x0-4)
所以周期是4

f(x+1)=g(x)=-g(-x)=-f(1-x)=f(1-x);所以f(x)的周期为2；
g(x)=f(x+1)=f(x-1)=g(x-2);所以g(x)的周期为2；