What is $$ (f \cdot g)(x) $$ ? $$ \begin{array}{l}f(x)=-3 x \ g(x)=3 x^{2}-7 x\end{array} $$ Write your answer as a polynomial or a rationa

Question

UpStudy AI · Accepted Answer

To find $$ (f \cdot g)(x) $$, we need to multiply the two functions $$ f(x) $$ and $$ g(x) $$.

Given:
- $$ f(x) = -3x $$
- $$ g(x) = 3x^2 - 7x $$

We can express $$ (f \cdot g)(x) $$ as follows:

$$
(f \cdot g)(x) = f(x) \cdot g(x) = (-3x) \cdot (3x^2 - 7x)
$$

Now, let's perform the multiplication step by step:

1. Distribute $$ -3x $$ to each term in $$ g(x) $$:
   - $$ -3x \cdot 3x^2 $$
   - $$ -3x \cdot (-7x) $$

Now, let's calculate these products:

$$
-3x \cdot 3x^2 = -9x^3
$$
$$
-3x \cdot (-7x) = 21x^2
$$

Combining these results, we have:

$$
(f \cdot g)(x) = -9x^3 + 21x^2
$$

Thus, the final answer is:

$$
(f \cdot g)(x) = -9x^3 + 21x^2
$$
$$ (f \cdot g)(x) = -9x^3 + 21x^2 $$

What is ?

Write your answer as a polynomial or a rationa