对于xy都有f(x+y)=f(x)+f(y)且x>0都有f(x)
问题描述:
对于xy都有f(x+y)=f(x)+f(y)且x>0都有f(x)
答
设x =0Y=0则F(0)=2F(0),F(0)=0,设X=X,Y=-X,则F(0)=F(X)+F(-X),移项,为奇,-F(X)大于0,则F(-X)大于0,结合已知,增,F2=2F1=6,F3=F2+F1=9,则F-3=-F3=-9