Determine which of the following conditions describe subspaces of the vector space C 1 consisting of all

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Determine which of the following conditions describe subspaces of the vector space C1 consisting of all continuously differentiable scalar functions f(x).
(a) f(2) = f(3),

(b) f′(2) = f(3),

(c) f′(x) + f(x) = 0,

(d) f(2 − x) = f(x),
(e) f(x + 2) = f(x) + 2,

(f) f(−x) = ex f(x).

(g) f(x) = a + b |x| for some a, b ∈ R,

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Applied Linear Algebra

ISBN: 9783319910406

2nd Edition

Authors: Peter J. Olver, Chehrzad Shakiban

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