Checking additive closure for a subspace

Question

Let $V = \{f \mid f:X \to K\}$ be a vector space over the field $K$. Let $U = \{f \mid f(5) = 1+f(4)\}$. Is this a subspace of $V$?

Well, clearly $U$ is non-empty. Take $f(x) =x$. Now additive closure? Let $h(x) = f(x)+g(x)$ where $f,g \in U$. Then $h(5) = (f+g)(5) = f(5) + g(5) = 2 + f(4)+g(4)$. How do I know if this is or is not in $U$?

Answer 1

It is not a subspace since $0\notin U$... (unless $K$ is a field with 1 element).