To determine [tex]\((p+q)(2)\)[/tex], we need to find the values [tex]\(p(2)\)[/tex] and [tex]\(q(2)\)[/tex] from the given tables and then calculate the sum of these values.
First, let's find [tex]\(p(2)\)[/tex] from the first table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & p(x) \\
\hline
4 & -1 \\
\hline
2 & 3 \\
\hline
-3 & 2 \\
\hline
\end{array}
\][/tex]
From the table, we see that when [tex]\(x = 2\)[/tex], [tex]\(p(x) = 3\)[/tex]. Therefore, [tex]\(p(2) = 3\)[/tex].
Next, let's find [tex]\(q(2)\)[/tex] from the second table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & q(x) \\
\hline
4 & 1 \\
\hline
2 & -2 \\
\hline
-3 & 5 \\
\hline
\end{array}
\][/tex]
From this table, we see that when [tex]\(x = 2\)[/tex], [tex]\(q(x) = -2\)[/tex]. Therefore, [tex]\(q(2) = -2\)[/tex].
Now, to find [tex]\((p+q)(2)\)[/tex], we simply add [tex]\(p(2)\)[/tex] and [tex]\(q(2)\)[/tex]:
[tex]\[
(p+q)(2) = p(2) + q(2) = 3 + (-2)
\][/tex]
Perform the addition:
[tex]\[
3 + (-2) = 1
\][/tex]
Therefore, [tex]\((p+q)(2) = 1\)[/tex].
