Answer :
To find \( x \) when \( f(x) = -3 \) using the given table, we need to look for the value of \( x \) in the table where the function \( f(x) \) equals -3. Here is the table for your 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]
We analyze each row to find when \( f(x) = -3 \):
- At \( x = -4 \), \( f(-4) = -66 \)
- At \( x = -3 \), \( f(-3) = -29 \)
- At \( x = -2 \), \( f(-2) = -10 \)
- At \( x = -1 \), \( f(-1) = -3 \)
- At \( x = 0 \), \( f(0) = -2 \)
- At \( x = 1 \), \( f(1) = -1 \)
- At \( x = 2 \), \( f(2) = 6 \)
From the table, we see that \( f(x) = -3 \) when \( x = -1 \).
Therefore, the value of \( x \) when \( f(x) = -3 \) is:
[tex]\[ \boxed{-1} \][/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 analyze each row to find when \( f(x) = -3 \):
- At \( x = -4 \), \( f(-4) = -66 \)
- At \( x = -3 \), \( f(-3) = -29 \)
- At \( x = -2 \), \( f(-2) = -10 \)
- At \( x = -1 \), \( f(-1) = -3 \)
- At \( x = 0 \), \( f(0) = -2 \)
- At \( x = 1 \), \( f(1) = -1 \)
- At \( x = 2 \), \( f(2) = 6 \)
From the table, we see that \( f(x) = -3 \) when \( x = -1 \).
Therefore, the value of \( x \) when \( f(x) = -3 \) is:
[tex]\[ \boxed{-1} \][/tex]
