## Elementary Linear Algebra 7th Edition

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