Calculate [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]



Answer :

To solve this problem, we need to identify the correct expression for [tex]\((f-g)(x)\)[/tex] from the given options. The expressions given 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]

Given that [tex]\((f-g)(x) = x^2 + x - 4\)[/tex], we need to determine which of the expressions matches this result.

Let's examine each option step-by-step:

1. Check the first option [tex]\(x^2 + x - 4\)[/tex]:
[tex]\[ x^2 + x - 4 \][/tex]
This exactly matches the given [tex]\((f-g)(x)\)[/tex].

2. Check the second option [tex]\(x^2 + x + 4\)[/tex]:
[tex]\[ x^2 + x + 4 \][/tex]
This does not match the given [tex]\(x^2 + x - 4\)[/tex].

3. Check the third option [tex]\(x^2 - x + 6\)[/tex]:
[tex]\[ x^2 - x + 6 \][/tex]
This does not match the given [tex]\(x^2 + x - 4\)[/tex].

4. Check the fourth option [tex]\(x^2 + x + 6\)[/tex]:
[tex]\[ x^2 + x + 6 \][/tex]
This does not match the given [tex]\(x^2 + x - 4\)[/tex].

From the comparison, the first expression [tex]\(x^2 + x - 4\)[/tex] is the only one that matches the given [tex]\((f-g)(x)\)[/tex].

Therefore, the correct expression for [tex]\((f-g)(x)\)[/tex] is the first one, and its index is [tex]\(0\)[/tex].