Question

已知函数y=f(x),对于任意实数a,b.都有f(ab)=af(b)+bf(a)成立

Answer 1

令a=b=0,则f(0*0)=f(0)=0f(0)+0f(0)=0,即f(0)=0

令a=b=1,则f(1*1)=f(1)=1*f(1)+1*f(1)=2f(1),即f(1)=0