如果f(xy)=f(x)×f(y)对一切实数x与y都成立,并且f(0)不等于0,则f(2005)=_______数学解答

如果f(xy)=f(x)×f(y)对一切实数x与y都成立,并且f(0)不等于0,则f(2005)=______

人气：321 ℃　时间：2020-04-09 07:49:10

解答

令x=y=0,由f(xy)=f(x)×f(y)得f(0)=f(0×0)=f(0)*f(0)=[f(0)]^2f(0)×[1-f(0)]=0因f(0)≠0,故f(0)=1.令x=2005,y=0,得f(2005×0)=f(0)=f(2005)×f(0)也即1=f(2005)×1故f(2005)=1.事实上本例中,令y=0,可得f(x×0)=f(0...