To compute \((f \cdot g)(x)\), where \(f(x)\) and \(g(x)\) are two functions, we perform the following steps:

1. **Multiply the functions \(f(x)\) and \(g(x)\)** together.
   
   \[
   (f \cdot g)(x) = f(x) \times g(x)
   \]

2. **Simplify the expression if possible.**

For example, if \(f(x) = 2x + 3\) and \(g(x) = x^2 - 1\), then:

\[
(f \cdot g)(x) = (2x + 3) \times (x^2 - 1)
\]

Expanding this:

\[
(f \cdot g)(x) = 2x(x^2) + 2x(-1) + 3(x^2) + 3(-1)
\]

Simplifying:

\[
(f \cdot g)(x) = 2x^3 - 2x + 3x^2 - 3
\]

So, \((f \cdot g)(x) = 2x^3 + 3x^2 - 2x - 3\).

If you provide the specific forms of \(f(x)\) and \(g(x)\), I can compute their product explicitly.

Would you like more details or have any questions?

Here are some related questions:
1. What is the product of \(f(x) = x + 2\) and \(g(x) = x - 3\)?
2. How do you find the derivative of the product \((f \cdot g)(x)\)?
3. What happens if you multiply a polynomial function by a constant function?
4. Can the product of two functions ever be a constant function?
5. How does the domain of \((f \cdot g)(x)\) relate to the domains of \(f(x)\) and \(g(x)\)?

**Tip:** Always consider the domain of the functions when multiplying them, as it could affect the domain of the resulting function.

Explore the method to compute the product of two functions, (f * g)(x), with a detailed example of multiplying polynomial functions. Understand key algebraic concepts, including function multiplication and polynomial expansion. Perfect for students in Grades 9-11.

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