Sure, let's break down the process step-by-step in detail.
Given the function [tex]\( f(g) \)[/tex]:
1. Initially, we have the expression:
[tex]\[
f(g) = 3x - 2
\][/tex]
2. Next, we substitute [tex]\( g \)[/tex] with [tex]\( x + 1 \)[/tex] because [tex]\( g = x + 1 \)[/tex]. Therefore, the expression becomes:
[tex]\[
f(g) = 3(x + 1) - 2
\][/tex]
3. Now, let's simplify the expression inside the parentheses:
[tex]\[
f(g) = 3x + 3 - 2
\][/tex]
4. Finally, we combine like terms to get the simplified expression:
[tex]\[
f(g) = 3x + 1
\][/tex]
Thus, the final result of [tex]\( f(g) \)[/tex] is [tex]\( 3x + 1 \)[/tex].
To summarize, here are the steps:
[tex]\[
\begin{aligned}
f(g) & = 3x - 2 \\
& = 3(x + 1) - 2 \\
& = 3x + 3 - 2 \\
& = 3x + 1
\end{aligned}
\][/tex]
This concludes the step-by-step solution.
