Certainly! Let's complete the table step-by-step.
1. Given [tex]\( g(x) = 7 \)[/tex]:
Start with the equation [tex]\( g(x) = -4x - 1 \)[/tex].
We need to solve for [tex]\( x \)[/tex]:
[tex]\[
7 = -4x - 1
\][/tex]
Add 1 to both sides:
[tex]\[
8 = -4x
\][/tex]
Divide both sides by -4:
[tex]\[
x = -2
\][/tex]
So, when [tex]\( g(x) = 7 \)[/tex], [tex]\( x = -2 \)[/tex].
2. Given [tex]\( x = 0 \)[/tex]:
We need to find [tex]\( g(0) \)[/tex]:
[tex]\[
g(0) = -4(0) - 1 = -1
\][/tex]
So, when [tex]\( x = 0 \)[/tex], [tex]\( g(x) = -1 \)[/tex].
3. Given [tex]\( x = -1 \)[/tex]:
We need to find [tex]\( g(-1) \)[/tex]:
[tex]\[
g(-1) = -4(-1) - 1 = 4 - 1 = 3
\][/tex]
So, when [tex]\( x = -1 \)[/tex], [tex]\( g(x) = 3 \)[/tex].
4. The row with an empty [tex]\( x \)[/tex] value:
Since we are given no additional information for this row, we cannot determine the value of [tex]\( x \)[/tex] or [tex]\( g(x) \)[/tex]. This row will remain incomplete.
Now, let's complete the table with the values we have found:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $g(x)$ \\
\hline
-2 & 7 \\
\hline
0 & -1 \\
\hline
-1 & 3 \\
\hline
& \\
\hline
\end{tabular}
\][/tex]
