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Question: Determine if the given subset is a subspace of the given vector space. Prove your claim.
Question: (a) Is the set P of all polynomials of the form p(x) = a+x2, with a ? R, a subspace of P2?
Question: (b) Is the set O of all odd functions in F, that is, O = {f ? F | f(?x) = ?f(x), for all x ? R}, a subspace of the vector space F of all functions from R to R?
Recall that in class we showed that F is a vector space for the usual addition of functions ((f + g)(x) = f (x) + g(x)) and the usual scalar multiplication of functions by real numbers ((cf)(x) = cf(x)).
Solve this question and show each and every step in detail.
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