Answer
The set $W$ of all exponential functions $f(x)=a^{x}$
where $a>0$ is not a vector subspace of $C(-\infty, \infty)$.
Work Step by Step
The set $W$ of all exponential functions $f(x)=a^{x}$
where $a>0$ is not a vector subspace of $C(-\infty, \infty)$. Because it is not closed under neither scalar multiplication nor addition.