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Answer :
To find [tex]\((f \cdot g)(x)\)[/tex], we'll multiply the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] together.
1. The functions given are:
- [tex]\(f(x) = x + 4\)[/tex]
- [tex]\(g(x) = 3x^2 - 7\)[/tex]
2. To multiply these, we use the distributive property:
[tex]\[
(f \cdot g)(x) = (x + 4) \cdot (3x^2 - 7)
\][/tex]
3. Distribute each term in the first bracket by each term in the second bracket:
- First, multiply [tex]\(x\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
[tex]\[
x \cdot (3x^2 - 7) = 3x^3 - 7x
\][/tex]
- Next, multiply [tex]\(4\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
[tex]\[
4 \cdot (3x^2 - 7) = 12x^2 - 28
\][/tex]
4. Add all these products together:
[tex]\[
3x^3 - 7x + 12x^2 - 28
\][/tex]
5. Combine like terms:
- The final expression is already simplified:
[tex]\[
3x^3 + 12x^2 - 7x - 28
\][/tex]
6. Therefore, the answer is:
[tex]\[
(f \cdot g)(x) = 3x^3 + 12x^2 - 7x - 28
\][/tex]
So, the correct choice is:
- A. [tex]\((f \cdot g)(x) = 3x^3 + 12x^2 - 7x - 28\)[/tex]
1. The functions given are:
- [tex]\(f(x) = x + 4\)[/tex]
- [tex]\(g(x) = 3x^2 - 7\)[/tex]
2. To multiply these, we use the distributive property:
[tex]\[
(f \cdot g)(x) = (x + 4) \cdot (3x^2 - 7)
\][/tex]
3. Distribute each term in the first bracket by each term in the second bracket:
- First, multiply [tex]\(x\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
[tex]\[
x \cdot (3x^2 - 7) = 3x^3 - 7x
\][/tex]
- Next, multiply [tex]\(4\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
[tex]\[
4 \cdot (3x^2 - 7) = 12x^2 - 28
\][/tex]
4. Add all these products together:
[tex]\[
3x^3 - 7x + 12x^2 - 28
\][/tex]
5. Combine like terms:
- The final expression is already simplified:
[tex]\[
3x^3 + 12x^2 - 7x - 28
\][/tex]
6. Therefore, the answer is:
[tex]\[
(f \cdot g)(x) = 3x^3 + 12x^2 - 7x - 28
\][/tex]
So, the correct choice is:
- A. [tex]\((f \cdot g)(x) = 3x^3 + 12x^2 - 7x - 28\)[/tex]
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