Answer :
To find the value of [tex]\((p+q)(2)\)[/tex] using the given tables, we need to evaluate the expressions for both [tex]\(p(2)\)[/tex] and [tex]\(q(2)\)[/tex] and then add them together. Let's break this down step-by-step:
1. First, we look at the table for [tex]\(p(x)\)[/tex]. Locate the row where [tex]\(x = 2\)[/tex]:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $p(x)$ \\ \hline 4 & -1 \\ \hline 2 & 3 \\ \hline -3 & 2 \\ \hline \end{tabular} \][/tex]
From this table, we see that [tex]\(p(2) = 3\)[/tex].
2. Next, we look at the table for [tex]\(q(x)\)[/tex]. Locate the row where [tex]\(x = 2\)[/tex]:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $q(x)$ \\ \hline 4 & 1 \\ \hline 2 & -2 \\ \hline -3 & 5 \\ \hline \end{tabular} \][/tex]
From this table, we see that [tex]\(q(2) = -2\)[/tex].
3. Now, we simply add the values found in the previous steps:
[tex]\[ (p+q)(2) = p(2) + q(2) = 3 + (-2) = 1 \][/tex]
So, the value of [tex]\((p+q)(2)\)[/tex] is:
[tex]\[ (p+q)(2) = 1 \][/tex]
1. First, we look at the table for [tex]\(p(x)\)[/tex]. Locate the row where [tex]\(x = 2\)[/tex]:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $p(x)$ \\ \hline 4 & -1 \\ \hline 2 & 3 \\ \hline -3 & 2 \\ \hline \end{tabular} \][/tex]
From this table, we see that [tex]\(p(2) = 3\)[/tex].
2. Next, we look at the table for [tex]\(q(x)\)[/tex]. Locate the row where [tex]\(x = 2\)[/tex]:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $q(x)$ \\ \hline 4 & 1 \\ \hline 2 & -2 \\ \hline -3 & 5 \\ \hline \end{tabular} \][/tex]
From this table, we see that [tex]\(q(2) = -2\)[/tex].
3. Now, we simply add the values found in the previous steps:
[tex]\[ (p+q)(2) = p(2) + q(2) = 3 + (-2) = 1 \][/tex]
So, the value of [tex]\((p+q)(2)\)[/tex] is:
[tex]\[ (p+q)(2) = 1 \][/tex]
