Answer :
To find [tex]\((f \cdot g)(x)\)[/tex], we need to multiply the two functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]. The functions given are:
[tex]\[ f(x) = x + 4 \][/tex]
[tex]\[ g(x) = 3x^2 - 7 \][/tex]
The product [tex]\((f \cdot g)(x)\)[/tex] is calculated by multiplying [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[
(f \cdot g)(x) = (x + 4)(3x^2 - 7)
\][/tex]
To do this, we'll use the distributive property and distribute each term in [tex]\(f(x)\)[/tex] across each term in [tex]\(g(x)\)[/tex]:
1. Multiply [tex]\(x\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
- [tex]\(x \times 3x^2 = 3x^3\)[/tex]
- [tex]\(x \times (-7) = -7x\)[/tex]
2. Multiply [tex]\(4\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
- [tex]\(4 \times 3x^2 = 12x^2\)[/tex]
- [tex]\(4 \times (-7) = -28\)[/tex]
Now, combine all the terms:
[tex]\[
3x^3 + 12x^2 - 7x - 28
\][/tex]
So, the expression for [tex]\((f \cdot g)(x)\)[/tex] is:
[tex]\[
(f \cdot g)(x) = 3x^3 + 12x^2 - 7x - 28
\][/tex]
The correct answer is:
A. [tex]\((f \cdot g)(x) = 3x^3 + 12x^2 - 7x - 28\)[/tex]
[tex]\[ f(x) = x + 4 \][/tex]
[tex]\[ g(x) = 3x^2 - 7 \][/tex]
The product [tex]\((f \cdot g)(x)\)[/tex] is calculated by multiplying [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[
(f \cdot g)(x) = (x + 4)(3x^2 - 7)
\][/tex]
To do this, we'll use the distributive property and distribute each term in [tex]\(f(x)\)[/tex] across each term in [tex]\(g(x)\)[/tex]:
1. Multiply [tex]\(x\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
- [tex]\(x \times 3x^2 = 3x^3\)[/tex]
- [tex]\(x \times (-7) = -7x\)[/tex]
2. Multiply [tex]\(4\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
- [tex]\(4 \times 3x^2 = 12x^2\)[/tex]
- [tex]\(4 \times (-7) = -28\)[/tex]
Now, combine all the terms:
[tex]\[
3x^3 + 12x^2 - 7x - 28
\][/tex]
So, the expression for [tex]\((f \cdot g)(x)\)[/tex] is:
[tex]\[
(f \cdot g)(x) = 3x^3 + 12x^2 - 7x - 28
\][/tex]
The correct answer is:
A. [tex]\((f \cdot g)(x) = 3x^3 + 12x^2 - 7x - 28\)[/tex]
