Answer
$W$ is not a vector subspace of $C(-\infty, \infty)$.
Work Step by Step
Let $f(x)=x+1, g(x)=-x+2\in W$. Now, $$f(x)+ g(x)=3$$
which means that $W$ is not closed under addition. Hence, $W$ is not vector subspace of $C(-\infty, \infty)$.
Elementary Linear Algebra 7th Edition
by Larson, Ron
Published by
Cengage Learning
ISBN 10:
1-13311-087-8
ISBN 13:
978-1-13311-087-3
Chapter 4 - Vector Spaces - 4.3 Subspaces of Vector Spaces - 4.3 Exercises - Page 167: 12
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