To find [tex]\((p + q)(2)\)[/tex], we will utilize the given tables for the functions [tex]\(p(x)\)[/tex] and [tex]\(q(x)\)[/tex].
The tables provided are:
For [tex]\(p(x)\)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & p(x) \\
\hline
4 & -1 \\
2 & 3 \\
-3 & 2 \\
\hline
\end{array}
\][/tex]
For [tex]\(q(x)\)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & q(x) \\
\hline
4 & 1 \\
2 & -2 \\
-3 & 5 \\
\hline
\end{array}
\][/tex]
Now, to find [tex]\((p + q)(2)\)[/tex]:
1. First, determine the value of [tex]\(p(2)\)[/tex]:
[tex]\[
p(2) = 3
\][/tex]
2. Next, determine the value of [tex]\(q(2)\)[/tex]:
[tex]\[
q(2) = -2
\][/tex]
3. Add these values to find [tex]\((p + q)(2)\)[/tex]:
[tex]\[
(p + q)(2) = p(2) + q(2) = 3 + (-2) = 1
\][/tex]
Therefore, the value of [tex]\((p + q)(2)\)[/tex] is [tex]\(1\)[/tex].
