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Thread: Prove even functions set is a vector space

  1. #1
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    Prove even functions set is a vector space

    Prove that set of even functions under addition and scalar multiplication is a vector space.

    Proof. Let F denote the set of functions f with f(t) = f(-t) for all t.

    Now let f and g be in F, then (f+g) (t) = f(t) + g(t), (fog)(t) = f(g(t)).

    Is that enough to prove that it is a vector space?
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Prove that set of even functions under addition and scalar multiplication is a vector space.

    Proof. Let F denote the set of functions f with f(t) = f(-t) for all t.

    Now let f and g be in F, then (f+g) (t) = f(t) + g(t), (fog)(t) = f(g(t)).

    Is that enough to prove that it is a vector space?
    If f,g are even then f+g is even and kf is even where k\in \mathbb{R}. So it is a vector space.
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