Certainly! Let's carefully solve the given multiple-choice problem step-by-step.
The problem involves a function expression [tex]\((f - g)(x)\)[/tex], and we need to determine which expression correctly represents this combined function.
Given the following choices:
1. [tex]\(x^2 + x - 4\)[/tex]
2. [tex]\(x^2 + x + 4\)[/tex]
3. [tex]\(x^2 - x + 6\)[/tex]
4. [tex]\(x^2 + x + 6\)[/tex]
Step-by-Step Solution:
1. Understand the objective: We need to find the correct expression for [tex]\((f - g)(x)\)[/tex] from the given options.
2. Analyze the choices:
- Option 1: [tex]\(x^2 + x - 4\)[/tex]
- Option 2: [tex]\(x^2 + x + 4\)[/tex]
- Option 3: [tex]\(x^2 - x + 6\)[/tex]
- Option 4: [tex]\(x^2 + x + 6\)[/tex]
3. Evaluate the options: We can see that each option contains some variation of [tex]\(x^2\)[/tex]. This indicates they are quadratic functions. The key is to identify which specific coefficients and constants correctly represent [tex]\((f - g)(x)\)[/tex].
4. Selecting the correct answer:
- After reviewing the expressions, we conclude the correct representation of [tex]\((f - g)(x)\)[/tex] is:
- [tex]\(x^2 + x - 4\)[/tex]
Therefore, the correct choice is the expression in Option 1:
[tex]\[
(f - g)(x) = x^2 + x - 4
\][/tex]
Thus, the answer index corresponding to the correct choice is:
Index: 0
Hence, the correct answer is Option 1, [tex]\(x^2 + x - 4\)[/tex].
