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If [tex] f(x) = 3x + 2 [/tex] and [tex] g(x) = 2x - 2 [/tex], what is [tex] (f - g)(x) [/tex]?

A. [tex] x + 4 [/tex]

B. [tex] x - 2 [/tex]

C. [tex] x [/tex]

D. [tex] 5x - 2 [/tex]

E. [tex] x = 4 [/tex]

Sagot :

GinnyAnswer
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]
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