To solve for the value of [tex]\( x \)[/tex] when [tex]\( f(x) = -3 \)[/tex], we can refer to the given table of values of the function [tex]\( f(x) \)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-4 & -66 \\
\hline
-3 & -29 \\
\hline
-2 & -10 \\
\hline
-1 & -3 \\
\hline
0 & -2 \\
\hline
1 & -1 \\
\hline
2 & 6 \\
\hline
\end{array}
\][/tex]
We need to find the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = -3 \)[/tex].
1. Look through the function values [tex]\( f(x) \)[/tex] in the table.
2. Identify the row where [tex]\( f(x) = -3 \)[/tex].
By going through each row:
- For [tex]\( x = -4 \)[/tex], [tex]\( f(-4) = -66 \)[/tex]
- For [tex]\( x = -3 \)[/tex], [tex]\( f(-3) = -29 \)[/tex]
- For [tex]\( x = -2 \)[/tex], [tex]\( f(-2) = -10 \)[/tex]
- For [tex]\( x = -1 \)[/tex], [tex]\( f(-1) = -3 \)[/tex]
- For [tex]\( x = 0 \)[/tex], [tex]\( f(0) = -2 \)[/tex]
- For [tex]\( x = 1 \)[/tex], [tex]\( f(1) = -1 \)[/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( f(2) = 6 \)[/tex]
We find that [tex]\( f(-1) = -3 \)[/tex].
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( f(x) = -3 \)[/tex] is [tex]\( x = -1 \)[/tex].
The correct option is:
[tex]\[
\boxed{-1}
\][/tex]
