To solve for [tex]\((f - g)(x)\)[/tex] given the functions [tex]\(f(x) = 3x - 2\)[/tex] and [tex]\(g(x) = 2x + 1\)[/tex], we'll follow these steps:
1. Substitute the given functions into the expression [tex]\((f - g)(x)\)[/tex]:
[tex]\[
(f - g)(x) = f(x) - g(x)
\][/tex]
2. Plug in the definitions of [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[
(f - g)(x) = (3x - 2) - (2x + 1)
\][/tex]
3. Distribute the negative sign across the terms in the second function [tex]\(g(x)\)[/tex]:
[tex]\[
(f - g)(x) = 3x - 2 - 2x - 1
\][/tex]
4. Combine like terms:
[tex]\[
(f - g)(x) = (3x - 2x) + (-2 - 1)
\][/tex]
Simplify the terms inside the parentheses:
[tex]\[
(f - g)(x) = 1x - 3 = x - 3
\][/tex]
Therefore, the function [tex]\((f - g)(x)\)[/tex] simplifies to:
[tex]\((f - g)(x) = x - 3\)[/tex]
