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Find the value of [tex]\((f-g)(x)\)[/tex]:

A. [tex]\(x^2 + x - 4\)[/tex]
B. [tex]\(x^2 + x + 4\)[/tex]
C. [tex]\(x^2 - x + 6\)[/tex]
D. [tex]\(x^2 + x + 6\)[/tex]

Sagot :

GinnyAnswer
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].
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