The function [tex]\( f(x) = x^5 + (x+3)^2 \)[/tex] is used to create this table:

[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $f(x)$ \\
\hline
-2 & -31 \\
\hline
-1 & ? \\
\hline
0 & 9 \\
\hline
1 & 17 \\
\hline
\end{tabular}
\][/tex]

Which value completes the table?

A. -17
B. -3
C. 1
D. 3



Answer :

To complete the table, we need to find the value of the function [tex]\( f(x) = x^5 + (x + 3)^2 \)[/tex] at [tex]\( x = -1 \)[/tex].

1. Start by substituting [tex]\( x = -1 \)[/tex] into the function.
[tex]\[ f(-1) = (-1)^5 + (-1 + 3)^2 \][/tex]

2. Calculate [tex]\( (-1)^5 \)[/tex].
[tex]\[ (-1)^5 = -1 \][/tex]

3. Calculate [tex]\( (-1 + 3)^2 \)[/tex].
[tex]\[ -1 + 3 = 2 \][/tex]
[tex]\[ 2^2 = 4 \][/tex]

4. Add the results from the previous steps.
[tex]\[ f(-1) = -1 + 4 = 3 \][/tex]

Therefore, the value of [tex]\( f(-1) \)[/tex] is 3.

This means the complete table is:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline
-2 & -31 \\
\hline
-1 & 3 \\
\hline
0 & 9 \\
\hline
1 & 17 \\
\hline
\end{tabular}

The value that completes the table is [tex]\( 3 \)[/tex].