Let $f : X \to \operatorname{Spec}(A)$ be morphism of schemes. Let $g\in A$ .
Is it true that $f^{-1}(D_{A}(g))= X_{f^{\#}(\operatorname{Spec}(A))(g)}$.
where, $X_{f^{\#}(\operatorname{Spec}(A))(g)}=[x\in X : (f^{\#}(\operatorname{Spec}(A))(g))_{x}\notin m_{x}]$
I am not able to establish any inclusion between the two sets.
Please help, I am badly stuck at this.
Edit : I got the solution. One needs to consider affine open subsets of $X$ and just use the definitions.