To find [tex]\((p+q)(2)\)[/tex], we need to evaluate the sum of the functions [tex]\(p(x)\)[/tex] and [tex]\(q(x)\)[/tex] at [tex]\(x = 2\)[/tex].
First, let's determine the value of [tex]\(p(2)\)[/tex] from the given table for [tex]\(p(x)\)[/tex]:
[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 [tex]\(p(2) = 3\)[/tex].
Next, let's determine the value of [tex]\(q(2)\)[/tex] from the given table for [tex]\(q(x)\)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & q(x) \\
\hline
4 & 1 \\
\hline
2 & -2 \\
\hline
-3 & 5 \\
\hline
\end{array}
\][/tex]
From the table, we see that [tex]\(q(2) = -2\)[/tex].
Now, we add these values together to find [tex]\((p+q)(2)\)[/tex]:
[tex]\[
(p+q)(2) = p(2) + q(2)
\][/tex]
Substituting the values we found:
[tex]\[
(p+q)(2) = 3 + (-2)
\][/tex]
Simplifying the expression:
[tex]\[
(p+q)(2) = 3 - 2 = 1
\][/tex]
Therefore, [tex]\((p+q)(2) = 1\)[/tex].
