To determine the value of [tex]\( x \)[/tex] when [tex]\( f(x) = -3 \)[/tex] using the given table, follow these steps:
1. Understand the table:
The table shows pairs of [tex]\( x \)[/tex] and [tex]\( f(x) \)[/tex] values. We are looking for the value of [tex]\( x \)[/tex] where [tex]\( f(x) = -3 \)[/tex].
2. Scan the [tex]\( f(x) \)[/tex] values in the table:
Go through the [tex]\( f(x) \)[/tex] values to find [tex]\( -3 \)[/tex].
3. Identify the corresponding [tex]\( x \)[/tex] value:
Once we find [tex]\( f(x) = -3 \)[/tex], note the corresponding [tex]\( x \)[/tex] value.
Here is the given table for reference:
[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]
4. Find [tex]\( f(x) = -3 \)[/tex]:
- When [tex]\( x = -4 \)[/tex], [tex]\( f(x) = -66 \)[/tex]
- When [tex]\( x = -3 \)[/tex], [tex]\( f(x) = -29 \)[/tex]
- When [tex]\( x = -2 \)[/tex], [tex]\( f(x) = -10 \)[/tex]
- When [tex]\( x = -1 \)[/tex], [tex]\( f(x) = -3 (this matches our target \( f(x) \)[/tex])
Thus, the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = -3 \)[/tex] is:
[tex]\[ \boxed{-1} \][/tex]
