若函数f(x)满足f(x+y)=f(x)+f(y) (x,y∈R)证明f(-x)f(x)
2个回答
f(x+0)=f(x)+f(0)=f(x)
f(0)=0
f(x-x)=f(0)=f(x)+f(-x)=0
f(x)=-f(-x)
f(x)f(-x)=-[f(x)]^2
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