設函數f(x)在(-∞,+∞)內有定義,f(0)不等於0,f(xy)=f(x)f(y),證明:f(x)=1

設函數f(x)在(-∞,+∞)內有定義,f(0)不等於0,f(xy)=f(x)f(y),證明:f(x)=1

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