f(x+8)=f(x+4+4)=1/f(x+4)=f(x)
f(x)的周期为8
f(2011)=f(8*251+3)=f(3)=-f(-3)=-f(-3+8)=-f(5)=-f(1+4)=-1/f(1)=-1/2^1=-1/2