To solve the problem [tex]\((f - g)(x)\)[/tex] given the functions [tex]\( f(x) = x^2 + x + 6 \)[/tex] and [tex]\( g(x) = 4 \)[/tex], we need to follow these steps:
1. Define the functions:
- [tex]\( f(x) = x^2 + x + 6 \)[/tex]
- [tex]\( g(x) = 4 \)[/tex]
2. Subtraction of functions:
- We need to subtract [tex]\( g(x) \)[/tex] from [tex]\( f(x) \)[/tex].
- So, [tex]\( (f - g)(x) = f(x) - g(x) \)[/tex].
3. Perform the subtraction:
- [tex]\( f(x) - g(x) = (x^2 + x + 6) - 4 \)[/tex].
4. Simplify the expression:
- To subtract these, subtract 4 from the constant term in [tex]\( f(x) \)[/tex]:
- [tex]\( x^2 + x + 6 - 4 \)[/tex].
- Simplify the constant terms: [tex]\( 6 - 4 = 2 \)[/tex].
Therefore, the result of the subtraction [tex]\( (f - g)(x) \)[/tex] is:
[tex]\[ x^2 + x + 2 \][/tex].
So the correct answer is not among the given options. The correct and simplified form of [tex]\((f - g)(x)\)[/tex] is:
[tex]\[ x^2 + x + 2 \][/tex].
