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@jemoka / Jemoka Knowledge Base / raw/textbook/axler/kbhaxler_1_c_excercises.md
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--- title: "Axler 1.C Exercises" source: https://www.jemoka.com/posts/kbhaxler_1_c_excercises/ --- 3: Show that the set of differential real-valued functions \(f\) on the interval \((-4,4)\) such that \(f’(-1)=3f(2)\) is a subspace of \(\mathbb{R}^{(-4,4)}\) 4: Suppose \(b \in R\). Show that the set of continuous real-valued functions \(f\) on the interval \([0,1]\) such that \(\int_{0}^{1}f=b\) is a subspace of \(\mathbb{R}^{[0,1]}\) IFF \(b=0\) Additive Identity: assume \(\int_{0}^{1}f=b\) is a subspace