Answer :
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]
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]
