设函数f(x)满足f(x+y)=f(x)+f(y),(x,y)∈R,求证 1。f(0)=o 2.f(3)=3f(1) 3.f(1/2)=3f(1)
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f(x)满足f(x+y)=f(x)+f(y),(x,y)∈R,故有1.f(0)=f(0+0)=f(0)+f(0),f(0)=2f(0),得f(0)=02.f(2)=f(1+1)=f(1)+f(1)=2f(1),故f(3)=f(2+1)=f(2)+f(1)=2f(1)+f(1)=3f(1)3.f(1)=f(1/2+1/2)=f(1/2)+f(1/2)=2f(1/2),故f(1/2)=(1/2)f(1) 3小题似乎有问题.