令y=0,则f(x+0)=f(x)*f(0)
即f(x)=f(x)*f(0)
(1)当f(x)=0时,满足题意,所以,f(0)=0
(2)当f(x)≠0时,则:f(0)=1
所以,f(0)=0或f(0)=1;
当f(x)=0时,显然满足f(x)≧0;
当f(x)≠0时,令x=y=t/2,则:f(t/2+t/2)=f²(t/2)
即:f(t)=f²(t/2)
显然对任意t∈R,都有f(t)≧0
即f(x)≧0
综上,f(x)≧0
祝中秋快乐!如果不懂,请Hi我,
f(x)=f(x)*f(0)f(x)≠0,则等式两边同除f(x),得:1=f(0)