Complete the table of inputs and outputs for the given function.

[tex]\[ g(x) = 3 - 8x \][/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
x & g(x) \\
\hline
\square & 0 \\
\hline
0 & \square \\
\hline
\square & -5 \\
\hline
3 & \square \\
\hline
\end{tabular}
\][/tex]



Answer :

Sure, let's fill in the table by finding the corresponding [tex]\( x \)[/tex] and [tex]\( g(x) \)[/tex] for the given function [tex]\( g(x) = 3 - 8x \)[/tex].

1. Finding [tex]\( x \)[/tex] when [tex]\( g(x) = 0 \)[/tex]:
To find [tex]\( x \)[/tex] when [tex]\( g(x) = 0 \)[/tex], we need to solve the equation:
[tex]\[ 3 - 8x = 0 \][/tex]
Rearranging the equation to solve for [tex]\( x \)[/tex]:
[tex]\[ 8x = 3 \implies x = \frac{3}{8} \implies x = 0.375 \][/tex]

2. Finding [tex]\( g(x) \)[/tex] when [tex]\( x = 0 \)[/tex]:
To find [tex]\( g(x) \)[/tex] when [tex]\( x = 0 \)[/tex]:
[tex]\[ g(0) = 3 - 8 \cdot 0 \implies g(0) = 3 \][/tex]

3. Finding [tex]\( x \)[/tex] when [tex]\( g(x) = -5 \)[/tex]:
To find [tex]\( x \)[/tex] when [tex]\( g(x) = -5 \)[/tex], we need to solve the equation:
[tex]\[ 3 - 8x = -5 \][/tex]
Rearranging the equation to solve for [tex]\( x \)[/tex]:
[tex]\[ 3 + 5 = 8x \implies 8 = 8x \implies x = 1.0 \][/tex]

4. Finding [tex]\( g(x) \)[/tex] when [tex]\( x = 3 \)[/tex]:
To find [tex]\( g(x) \)[/tex] when [tex]\( x = 3 \)[/tex]:
[tex]\[ g(3) = 3 - 8 \cdot 3 \implies g(3) = 3 - 24 \implies g(3) = -21 \][/tex]

Now that we have the necessary values, we can fill in the table:

[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $g(x)$ \\ \hline 0.375 & 0 \\ \hline 0 & 3 \\ \hline 1.0 & -5 \\ \hline 3 & -21 \\ \hline \end{tabular} \][/tex]

So, the completed table is:

[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $g(x)$ \\ \hline 0.375 & 0 \\ \hline 0 & 3 \\ \hline 1.0 & -5 \\ \hline 3 & -21 \\ \hline \end{tabular} \][/tex]