Let X a non empty set, $F$ a field and $V$ the set of function of $X$ on $F$. If $f,g \in V$ and $\lambda \in F$ , $f +g ,\lambda f \in V$ are the functions such that $\forall x \in X$,
$(f+g)(x)=f(x)+g(x)$ and $(\lambda f)(x) = \lambda f(x)$.

How can i construct a basis if $X = \{x\_1,...,x\_n \}$.

I really stuck in this problem some help please.