The following table lists the values of functions $f$ and $g$, and of their derivatives, $f^{\prime}$ and $g^{\prime}$, for the $x$-values 0 and 3 . \begin{tabular}{ccccc} $x$ & $f(x)$ & $g(x)$ & $f^{\prime}(x)$ & $g^{\prime}(x)$ \\ \hline 0 & 0 & -3 & 2 & 1 \\ 3 & -3 & 0 & -4 & 1 \end{tabular} Let function $F$ be defined as $F(x)=f(g(x))$. $F^{\prime}(3)=$

Step 1 ：Use the chain rule to find \(F^{\prime}(x)\), which gives \(F^{\prime}(x) = f^{\prime}(g(x)) \cdot g^{\prime}(x)\).

Step 2 ：Substitute \(x=3\) into the equation to get \(F^{\prime}(3) = f^{\prime}(g(3)) \cdot g^{\prime}(3)\).

Step 3 ：From the table, we know that \(g(3) = 0\) and \(g^{\prime}(3) = 1\).

Step 4 ：Substitute these values into the equation to get \(F^{\prime}(3) = f^{\prime}(0) \cdot 1\).

Step 5 ：From the table, we know that \(f^{\prime}(0) = 2\), so \(F^{\prime}(3) = 2 \cdot 1 = 2\).

Step 6 ：Therefore, \(\boxed{F^{\prime}(3) = 2}\).