1.
Let f: R --->R be a real function such that
f(x+y)=f(x)f(y) for all x, y belongs to R.
if f(x) is not identically equal to zero, show f(0)>0.
Hint: Assume for all x belongs to real such that f(x0)=0.
2. show f(x)=2x is not surjective
pure maths function
2009-03-08 7:34 am
回答 (1)
2009-03-08 8:23 am
✔ 最佳答案
1 If f(x) is not identically equal to zero, there should be at least a point a such that f(a) <>0Now f(a+0)=f(a)f(0)=>f(0)=1=>f(0)>0
2 show f(x)=2x is not surjective in Z
Consider 3 , you cannot find x in Z such that 2x=3,so f(x)=2x is not surjective
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