Answer :
To find [tex]\((f+g)(x)\)[/tex], we need to sum the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].
Given:
[tex]\[ f(x) = -x^2 + 6x - 1 \][/tex]
[tex]\[ g(x) = 3x^2 - 4x - 1 \][/tex]
First, let's sum these two functions:
[tex]\[ (f + g)(x) = f(x) + g(x) \][/tex]
So,
[tex]\[ (f + g)(x) = (-x^2 + 6x - 1) + (3x^2 - 4x - 1) \][/tex]
Next, we combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-x^2 + 3x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(6x - 4x\)[/tex]
- Combine the constant terms: [tex]\(-1 - 1\)[/tex]
Perform the additions:
[tex]\[ -x^2 + 3x^2 = 2x^2 \][/tex]
[tex]\[ 6x - 4x = 2x \][/tex]
[tex]\[ -1 - 1 = -2 \][/tex]
Putting it all together, we get:
[tex]\[ (f + g)(x) = 2x^2 + 2x - 2 \][/tex]
Thus, the correct choice is:
[tex]\[ \boxed{B: (f+g)(x) = 2x^2 + 2x - 2} \][/tex]
Given:
[tex]\[ f(x) = -x^2 + 6x - 1 \][/tex]
[tex]\[ g(x) = 3x^2 - 4x - 1 \][/tex]
First, let's sum these two functions:
[tex]\[ (f + g)(x) = f(x) + g(x) \][/tex]
So,
[tex]\[ (f + g)(x) = (-x^2 + 6x - 1) + (3x^2 - 4x - 1) \][/tex]
Next, we combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-x^2 + 3x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(6x - 4x\)[/tex]
- Combine the constant terms: [tex]\(-1 - 1\)[/tex]
Perform the additions:
[tex]\[ -x^2 + 3x^2 = 2x^2 \][/tex]
[tex]\[ 6x - 4x = 2x \][/tex]
[tex]\[ -1 - 1 = -2 \][/tex]
Putting it all together, we get:
[tex]\[ (f + g)(x) = 2x^2 + 2x - 2 \][/tex]
Thus, the correct choice is:
[tex]\[ \boxed{B: (f+g)(x) = 2x^2 + 2x - 2} \][/tex]
