Let's complete the table step by step.
1. To find [tex]\( x \)[/tex] when [tex]\( g(x) = 7 \)[/tex]:
Given the function [tex]\( g(x) = -4x - 1 \)[/tex], set [tex]\( g(x) = 7 \)[/tex]:
[tex]\[
7 = -4x - 1
\][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[
7 + 1 = -4x \implies 8 = -4x \implies x = \frac{8}{-4} \implies x = -2
\][/tex]
2. To find [tex]\( g(x) \)[/tex] when [tex]\( x = 0 \)[/tex]:
Substitute [tex]\( x = 0 \)[/tex] into [tex]\( g(x) = -4x - 1 \)[/tex]:
[tex]\[
g(0) = -4(0) - 1 = 0 - 1 = -1
\][/tex]
3. To find [tex]\( x \)[/tex] when [tex]\( g(x) = -13 \)[/tex]:
Given the function [tex]\( g(x) = -4x - 1 \)[/tex], set [tex]\( g(x) = -13 \)[/tex]:
[tex]\[
-13 = -4x - 1
\][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[
-13 + 1 = -4x \implies -12 = -4x \implies x = \frac{-12}{-4} \implies x = 3
\][/tex]
4. To find [tex]\( g(x) \)[/tex] when [tex]\( x = -1 \)[/tex]:
Substitute [tex]\( x = -1 \)[/tex] into [tex]\( g(x) = -4x - 1 \)[/tex]:
[tex]\[
g(-1) = -4(-1) - 1 = 4 - 1 = 3
\][/tex]
Now, we can complete the table as follows:
[tex]\[
\begin{tabular}{|c|c|}
\hline $x$ & $g(x)$ \\
\hline -2 & 7 \\
\hline 0 & -1 \\
\hline 3 & -13 \\
\hline -1 & 3 \\
\hline
\end{tabular}
\][/tex]
