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If [tex]f(x) = 7x - 1[/tex] and [tex]g(x) = x^3[/tex], find [tex](f \cdot g)(x)[/tex].

A. [tex]6x^3[/tex]
B. [tex]7x^4 - x^3[/tex]
C. [tex]7x^3 - 1[/tex]
D. [tex]7x^4 - 1[/tex]

Answer :

To find [tex]\((f \cdot g)(x)\)[/tex], where [tex]\(f(x) = 7x - 1\)[/tex] and [tex]\(g(x) = x^3\)[/tex], you need to multiply the two functions together. Here's how you can do it step-by-step:

1. Write down the expressions for each function:
- [tex]\(f(x) = 7x - 1\)[/tex]
- [tex]\(g(x) = x^3\)[/tex]

2. Calculate the product [tex]\((f \cdot g)(x)\)[/tex]:
- [tex]\((f \cdot g)(x) = f(x) \cdot g(x) = (7x - 1) \cdot x^3\)[/tex]

3. Distribute [tex]\(x^3\)[/tex] across the terms in [tex]\(f(x)\)[/tex]:
- Multiply [tex]\(7x\)[/tex] by [tex]\(x^3\)[/tex]: [tex]\(7x \cdot x^3 = 7x^{4}\)[/tex]
- Multiply [tex]\(-1\)[/tex] by [tex]\(x^3\)[/tex]: [tex]\(-1 \cdot x^3 = -x^3\)[/tex]

4. Combine the results from step 3:
- [tex]\((f \cdot g)(x) = 7x^4 - x^3\)[/tex]

So, the result of [tex]\((f \cdot g)(x)\)[/tex] is [tex]\(7x^4 - x^3\)[/tex].

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