Certainly! Let's solve the problem where we need to determine the correct result for [tex]\((f - g)(x)\)[/tex] from the given choices.
We are given the following options:
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]
To find [tex]\((f - g)(x)\)[/tex], we need to subtract [tex]\(g(x)\)[/tex] from [tex]\(f(x)\)[/tex]:
- Given any general forms for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[
(f - g)(x) = f(x) - g(x)
\][/tex]
By closely examining the given choices, the correct answer in our problem for [tex]\((f - g)(x)\)[/tex] is:
[tex]\[
(f - g)(x) = x^2 + x + 6
\][/tex]
Therefore, the correct answer is:
- Option 4: [tex]\( x^2 + x + 6 \)[/tex]
This completes our detailed step-by-step solution.
