To solve the problem of finding [tex]\((f - g)(x)\)[/tex] given the functions [tex]\(f(x) = 3x + 2\)[/tex] and [tex]\(g(x) = 2x - 2\)[/tex], let's break it down step-by-step:
1. Define the functions:
- [tex]\(f(x) = 3x + 2\)[/tex]
- [tex]\(g(x) = 2x - 2\)[/tex]
2. Find the expression for [tex]\((f - g)(x)\)[/tex]:
- [tex]\((f - g)(x)\)[/tex] means [tex]\(f(x) - g(x)\)[/tex].
3. Substitute [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] with their respective expressions:
- [tex]\((f - g)(x) = (3x + 2) - (2x - 2)\)[/tex]
4. Simplify the expression:
- First, distribute the negative sign to the terms inside the parentheses:
[tex]\[
(f - g)(x) = 3x + 2 - 2x + 2
\][/tex]
- Combine like terms:
[tex]\[
(f - g)(x) = (3x - 2x) + (2 + 2)
\][/tex]
- This simplifies to:
[tex]\[
(f - g)(x) = x + 4
\][/tex]
So, the simplified expression for [tex]\((f - g)(x)\)[/tex] is [tex]\(x + 4\)[/tex].
The correct answer is:
A. [tex]\(x + 4\)[/tex]
