Vector space

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Homework Statement


Do functions that vanish at the end points x=0 and x=L form a vector space ? How about periodic functions obeying f(L)=f(0)? How about functions that obey f(0)=4 ?
If the functions do not qualify , list the things that go wrong .


Homework Equations


All axioms defining the vector space .


The Attempt at a Solution


I tried to sketch some functions collapsed on point x=L and x=0 and superposed them . But , I don't know how to make a pointwise addition of 2 functions which I don't know the explicit forms .
I guess functions mentioned on the problem are violating the closure feature of a vector space.

I got really confused :confused::frown:
 

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