Let $E=[1,2,...n]$ where $n$ is an odd integer.

Question

Let $E=[1,2,...n]$ where $n$ is an odd integer. Let $V:$ vector space of all functions from $E$ to $\mathbb{R}^3$ such that $(f+g)(k)=f(k)+g(k)$ and $(\lambda f)(k)=\lambda f(k)$ where $k \in E$ and $f,g \in V$. We need to find the dimension of $V$. I am confused on how to check the linear independence of the functions in $V$. Help