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The problem asks to find \((f \cdot g)(x)\), where the functions \( f(x) = -5x + 3 \) and \( g(x) = 3x^2 \) are given. This operation refers to the multiplication of the two functions.

Let's compute:

\[
(f \cdot g)(x) = f(x) \cdot g(x)
\]

Substitute the expressions for \( f(x) \) and \( g(x) \):

\[
(f \cdot g)(x) = (-5x + 3) \cdot (3x^2)
\]

Now distribute the \( 3x^2 \) across the terms of \( f(x) \):

\[
(f \cdot g)(x) = (-5x)(3x^2) + (3)(3x^2)
\]

Simplify each term:

\[
(f \cdot g)(x) = -15x^3 + 9x^2
\]

Thus, the result is:

\[
(f \cdot g)(x) = -15x^3 + 9x^2
\]

Would you like further clarification or details? Here are some related questions:

1. How do you find the product of two functions in general?
2. What are the differences between function multiplication and composition?
3. Can you apply this method to other operations like division or subtraction of functions?
4. How can we simplify complex function multiplications involving higher-degree polynomials?
5. What are the graphical implications of multiplying two functions?

**Tip:** Always double-check the signs when distributing terms during multiplication to avoid errors.

What is (f · g)(x) where f(x) = -5x + 3 and g(x) = 3x^2?

Learn how to multiply the functions f(x) = -5x + 3 and g(x) = 3x^2. This solution demonstrates the use of algebraic function multiplication, applying the distributive property to simplify polynomial expressions. Suitable for students in Grades 11-12 Precalculus.

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