---
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 \(f&rsquo;(-1)=3f(2)\) 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
