设函数f(x)对任意实数x,y都有f(x+y)=f(x)+f(y),且x>0时,f(x)

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/17 06:04:34

f(x+y) = f(x) + f(y)
put x=y=0
f(0) = f(0) + f(0)
=> f(0) =0
put y=-x
f(0)= f(x) + f(-x)
f(x) = -f(x)
=>f(x)是奇函数
(2)
y> x
y = x+c ( where c>0)
f(y) = f(x+c)
= f(x) + f(c)
< f(x) ( f(c) < 0 )
f(x)是减函数
（3)
f(x+y) = f(x) + f(y)
put x=1,y=1
f(2) = f(1) + f(1)
= 2f(1) = -4
put x=1,y=2
f(3) = f(1) + f(2)
= -2 -4 = -6
f(x)是减函数
x∈[-3,3]
minf(x) = f(3) =-6
maxf(x) = f(-3) = -(-6) = 6

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