Show that $j_{*}j^{-1}\mathcal{F}_{x}=\mathcal{F}_{x}$ if $x\in Z$ and $0$ otherwise, if $j:Z\rightarrow X$ is a closed subscheme of $X$

Question

Let $X$ be a scheme and $j:Z\subseteq X$ be a closed subscheme. Let $\mathcal{F}$ be a sheaf of modules over $X$. Show that \begin{equation*} j_{*}j^{-1}\mathcal{F}_{x}=\left\{\begin{matrix}\mathcal{F}_{x} & \text{ if $x\in Z$}\\0 & \text{otherwise}\end{matrix}\right. \end{equation*} I think I can show that $j_{*}j^{-1}\mathcal{F}_{x}=0$ if $x\notin Z$ and $j_{*}j^{-1}\mathcal{F}_{x}=\mathcal{F}_{x}$ if $x$ is contained in $Z^{o}$ (the largest open subset of $Z$), but what do I do if $x\in Z\setminus Z^{o}$?