Answer
See below
Work Step by Step
Given $V$ is the vector space of all real-valued functions defined on the interval $[a, b]$, and $S$ is the subset of $V$
We can write set $S$ as $S=\{f \in V:f(a)=1\}$.
We can notice that $S=\{f:[a,b] \rightarrow R$ given by $f(x)=0 \forall x \in [a,b] \notin S$.
Hence $S$ is not a subspace of $V$
