To find [tex]\((p+q)(2)\)[/tex], we need to evaluate the functions [tex]\( p \)[/tex] and [tex]\( q \)[/tex] at [tex]\( x = 2 \)[/tex] and then add the results together. Here’s a step-by-step solution:
1. Determine [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 can see that [tex]\( p(2) = 3 \)[/tex].
2. Determine [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 can see that [tex]\( q(2) = -2 \)[/tex].
3. Add the values obtained:
[tex]\[
(p+q)(2) = p(2) + q(2)
\][/tex]
Substituting the values we found:
[tex]\[
(p+q)(2) = 3 + (-2) = 1
\][/tex]
Therefore, [tex]\((p+q)(2) = 1\)[/tex].
