对于一切实数X,Y,函数f(x)满足f(xy)=f(X)f(y) 且f(0)不等于0,求f(2010)

问题描述:

对于一切实数X,Y,函数f(x)满足f(xy)=f(X)f(y) 且f(0)不等于0,求f(2010)

f(0*0)=f(0)*f(0),f(0)不等于0,即f(0)=1
f(0*2010)=f(0)*f(2010)
则 f(0)=f(0)*f(2010)
即 f(2010)=1