## Elementary Linear Algebra 7th Edition

The set of all odd functions: $f(-x)=-f(x)$ is a vector subspace of $C(-\infty, \infty)$.
The set $W$ of all odd functions: $f(-x)=-f(x)$ is a vector subspace of $C(-\infty, \infty)$. Since the sum of two odd functions is odd and multiplying odd function by a real constant is odd, it is easy to see that $W$ contains the zero function and it is closed under addition and scalar multiplication.