Answer
The set $W$ of all functions such that $f(0)=1$ is not a vector subspace of $C(-\infty, \infty)$.
Work Step by Step
The set $W$ of all functions such that $f(0)=1$ is not a vector subspace of $C(-\infty, \infty)$. Let $f,g\in W$, then $f(0)=1, g(0)=1$. Now, $(f+g)(0)=f(0)+g(0)=1+1=2$ and hence $f+g$ does not belong to $W$.
