F(x+y)=fx+fy,且当x>0时,fx

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F(x+y)=fx+fy,且当x>0时,fxF(x+y)=fx+fy,且当x>0时,fxF(x+y)=fx+fy,且当x>0时,fx设x>yfx-fy=f(x-y+y)-fy=f(x-y)+fy-fy

F(x+y)=fx+fy,且当x>0时,fx
F(x+y)=fx+fy,且当x>0时,fx

F(x+y)=fx+fy,且当x>0时,fx
设x>y fx-fy=f(x-y+y)-fy=f(x-y)+fy-fy=f(x-y)<0
所以fx在R上是减函数.
f(0)+f(1)=f(1)
f(0)=0
f(x)+f(-x)=f(0)
f(x)=-f(-x),函数是奇函数.
最小值为f(3)=f(1)+ f(1) + f(1)=-2,最大值f(-3)=- f(3)=2