Question

F(x+y)=fx+fy,且当x>0时,fx

Answer 1

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