已知函数f(x)对任意实数x,y都有f(x+y)=f(x)+f(y),且当x>0时,f(x)=0,f(-1)=-2.
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已知函数f(x)对任意实数x,y都有f(x+y)=f(x)+f(y),且当x>0时,f(x)=0,f(-1)=-2.
求f(0)的值
求证f(x)是奇函数
求证f(x)是增函数
求f(x)在[-2,1]上的值域
求f(0)的值
求证f(x)是奇函数
求证f(x)是增函数
求f(x)在[-2,1]上的值域
put x=y=0
f(0) = 2f(0)
f(0) = 0
put y=-x
f(0) = f(x) +f(-x)
f(x) = -f(-x)
=> f is odd
I think 且当x>0时,f(x)>0
for y> x
y= x+k ( k>0)
f(y) = f(x+k)= f(x) + f(k)
> f(x) ( f(k) >0 )
f is increasing
put x=-1, y=-1
f(-2) = f(-1)+f(-1) = -4
f(1) = -f(-1) = -(-2) =2
f(x)在[-2,1]上的值域 = [-4,2]
f(0) = 2f(0)
f(0) = 0
put y=-x
f(0) = f(x) +f(-x)
f(x) = -f(-x)
=> f is odd
I think 且当x>0时,f(x)>0
for y> x
y= x+k ( k>0)
f(y) = f(x+k)= f(x) + f(k)
> f(x) ( f(k) >0 )
f is increasing
put x=-1, y=-1
f(-2) = f(-1)+f(-1) = -4
f(1) = -f(-1) = -(-2) =2
f(x)在[-2,1]上的值域 = [-4,2]
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