设函数f(x)在(-∞,+∞)内有定义,f(0)不等于0,f(xy)=f(x)f(y),证明:f(x)=1

问题描述:

设函数f(x)在(-∞,+∞)内有定义,f(0)不等于0,f(xy)=f(x)f(y),证明:f(x)=1

令x=y=0
f(0)=f(0)×f(0)
f(0)不等于0,
f(0)=1
令y=0
f(0)=f(x)×f(0)
f(x)=1