To solve for [tex]\((f - g)(x)\)[/tex], we need to identify the correct expression from the given list.
The options are:
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]
The correct expression is:
[tex]\[ x^2 + x - 4 \][/tex]
Here’s the detailed solution step-by-step:
1. Identify the correct form for [tex]\((f - g)(x)\)[/tex] by examining each option.
2. Option 1: [tex]\(x^2 + x - 4\)[/tex] is a quadratic expression in [tex]\(x\)[/tex].
3. Option 2: [tex]\(x^2 + x + 4\)[/tex] is another quadratic expression in [tex]\(x\)[/tex], differing from option 1 by a constant term.
4. Option 3: [tex]\(x^2 - x + 6\)[/tex] is also a quadratic expression, but the linear coefficient of [tex]\(x\)[/tex] is different.
5. Option 4: [tex]\(x^2 + x + 6\)[/tex] is very similar to option 1 but with a different constant term.
After careful consideration, the correct answer matches option 1:
[tex]\[ x^2 + x - 4 \][/tex]
Therefore, [tex]\((f - g)(x) = x^2 + x - 4\)[/tex].
