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October 4th, 2009, 04:46 PM   #1
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Sub Groups with real value functions -Question

Please help with the below problem.

Let F be the set of all real-valued functions with domain R and let F' be the subset of F consisting of those functions that have a nonzero value at every point in R. Is the subset F' a subgroup of the group F under addition?

My notes says it fails closure under addition. Can someone please explain why?
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October 4th, 2009, 10:46 PM   #2
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Re: Sub Groups with real value functions -Question

Take two constant functions: f(x)=-c and f(x)=c
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