对一切实数x、y,函数f(x)满足f(xy)=f(x)f(y)且f(0)≠0,则f(2006)的值为
问题描述：
对一切实数x、y,函数f(x)满足f(xy)=f(x)f(y)且f(0)≠0,则f(2006)的值为
答
f(xy)=f(x)f(y)
f(0)=f(0)*f(0)=f(0)^2
f(0)≠0
所以，f(0)=1
f(2006*0)=f(0)*f(2006)
f(0)=f(0)*f(2006)
f(2006)=1
答
令x=y=0
得f(0)=[f(0)]^2
由f(0)≠0
则f(0)=1
令x=2006 y=0
f(0)=f(2006)f(0)
f(2006)=1