To solve this problem, we need to multiply the functions [tex]\( f(x) = -6x \)[/tex] and [tex]\( g(x) = x + 4 \)[/tex]. We will follow a step-by-step approach to find the product of these functions.
1. Identify the functions:
- [tex]\( f(x) = -6x \)[/tex]
- [tex]\( g(x) = x + 4 \)[/tex]
2. Multiply the functions:
[tex]\[
(f \cdot g)(x) = f(x) \cdot g(x)
\][/tex]
Substitute the given expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[
(f \cdot g)(x) = (-6x) \cdot (x + 4)
\][/tex]
3. Distribute [tex]\(-6x\)[/tex] over the terms inside the parentheses:
[tex]\[
(f \cdot g)(x) = -6x \cdot x + (-6x) \cdot 4
\][/tex]
4. Perform the multiplication:
[tex]\[
-6x \cdot x = -6x^2
\][/tex]
[tex]\[
-6x \cdot 4 = -24x
\][/tex]
5. Combine the terms:
[tex]\[
(f \cdot g)(x) = -6x^2 - 24x
\][/tex]
So, the simplified expression for [tex]\( (f \cdot g)(x) \)[/tex] is:
[tex]\[
(f \cdot g)(x) = -6x^2 - 24x
\][/tex]
Therefore, the correct answer is:
A) [tex]\( (f \cdot g)(x) = -6x^2 - 24x \)[/tex]
