Answer :
To find [tex]\((f \cdot g)(x)\)[/tex], you need to multiply the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].
Given:
- [tex]\(f(x) = x + 4\)[/tex]
- [tex]\(g(x) = 3x^2 - 7\)[/tex]
Let's calculate [tex]\((f \cdot g)(x) = f(x) \times g(x)\)[/tex]:
1. Write out the multiplication:
[tex]\[
(f \cdot g)(x) = (x + 4)(3x^2 - 7)
\][/tex]
2. Distribute each term inside the parentheses:
- 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]
- 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]
3. Combine all the terms:
[tex]\[
3x^3 + 12x^2 - 7x - 28
\][/tex]
The correct answer is: D. [tex]\((f \cdot g)(x) = 3x^3 + 12x^2 - 7x - 28\)[/tex].
Given:
- [tex]\(f(x) = x + 4\)[/tex]
- [tex]\(g(x) = 3x^2 - 7\)[/tex]
Let's calculate [tex]\((f \cdot g)(x) = f(x) \times g(x)\)[/tex]:
1. Write out the multiplication:
[tex]\[
(f \cdot g)(x) = (x + 4)(3x^2 - 7)
\][/tex]
2. Distribute each term inside the parentheses:
- 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]
- 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]
3. Combine all the terms:
[tex]\[
3x^3 + 12x^2 - 7x - 28
\][/tex]
The correct answer is: D. [tex]\((f \cdot g)(x) = 3x^3 + 12x^2 - 7x - 28\)[/tex].
