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Let C(R) be the vector space of continuous functions from R to R with the usual...

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Advance Math

Let C(R) be the vector space of continuous functions from R to Rwith the usual addition and scalar multiplication. Determine if Wis a subspace of C(R). Show algebraically and explain your answersthoroughly.

a. W = C^n(R) = { f ∈ C(R) | f has a continuous nthderivative}

b. W = {f ∈ C^2(R) | f''(x) + f(x) = 0}

c. W = {f ∈ C(R) | f(-x) = f(x)}.

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a has a continuous nth derivative Let are continuous where denotes nth    See Answer
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