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Given [tex]$f(x)=2x-3$[/tex] and [tex]$g(x)=f(3x)$[/tex], which table represents [tex][tex]$g(x)$[/tex][/tex]?

\begin{tabular}{|l|l|}
\hline
[tex]$x$[/tex] & [tex]$g(x)$[/tex] \\
\hline
1 & -3 \\
\hline
2 & 3 \\
\hline
3 & 9 \\
\hline
\end{tabular}

\begin{tabular}{|l|l|}
\hline
[tex]$x$[/tex] & [tex]$g(x)$[/tex] \\
\hline
1 & -1 \\
\hline
2 & 1 \\
\hline
3 & 3 \\
\hline
\end{tabular}

\begin{tabular}{|l|l|}
\hline
[tex]$x$[/tex] & [tex]$g(x)$[/tex] \\
\hline
1 & 3 \\
\hline
2 & 6 \\
\hline
3 & 9 \\
\hline
\end{tabular}

\begin{tabular}{|l|l|}
\hline
[tex]$x$[/tex] & [tex]$g(x)$[/tex] \\
\hline
1 & 3 \\
\hline
2 & 9 \\
\hline
3 & 15 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To solve for [tex]\( g(x) \)[/tex], we use the definitions given:

1. [tex]\( f(x) = 2x - 3 \)[/tex]
2. [tex]\( g(x) = f(3x) \)[/tex]

We need to calculate [tex]\( g(x) \)[/tex] for different values of [tex]\( x \)[/tex]:

1. For [tex]\( x = 1 \)[/tex]:
[tex]\[ g(1) = f(3 \cdot 1) = f(3) \][/tex]
Then, calculate [tex]\( f(3) \)[/tex]:
[tex]\[ f(3) = 2 \cdot 3 - 3 = 6 - 3 = 3 \][/tex]
Therefore:
[tex]\[ g(1) = 3 \][/tex]

2. For [tex]\( x = 2 \)[/tex]:
[tex]\[ g(2) = f(3 \cdot 2) = f(6) \][/tex]
Then, calculate [tex]\( f(6) \)[/tex]:
[tex]\[ f(6) = 2 \cdot 6 - 3 = 12 - 3 = 9 \][/tex]
Therefore:
[tex]\[ g(2) = 9 \][/tex]

3. For [tex]\( x = 3 \)[/tex]:
[tex]\[ g(3) = f(3 \cdot 3) = f(9) \][/tex]
Then, calculate [tex]\( f(9) \)[/tex]:
[tex]\[ f(9) = 2 \cdot 9 - 3 = 18 - 3 = 15 \][/tex]
Therefore:
[tex]\[ g(3) = 15 \][/tex]

The correct table that represents [tex]\( g(x) \)[/tex] is:

[tex]\[ \begin{tabular}{|l|l|} \hline $x$ & $g(x)$ \\ \hline 1 & 3 \\ \hline 2 & 9 \\ \hline 3 & 15 \\ \hline \end{tabular} \][/tex]

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