The set of all continuous real-valued functions on an interval (a,b) is denoted by C(a,b) and is a vector subspace of the vector space of all functions on (a,b). Show that the space of all functions f(x) in C(a,b) such that f(0) = 0 is a subspace of C(a,b) but that the space of all functions f(x) in C(a,b) such that f(0) 1 is not a subspace of C(a,b)

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