The given two functions are f(x)=3x+4
 and g(x)=x2−2x
. What mathematical expression would be for the product of the two functions (f∙g)(x)
?

Question 29Answer

3x3−2x2−8x


3x3+4x2−4x


3x3+4x2−8x


3x3−2x2+4x

To find the product of two functions, \( (f \cdot g)(x) \), you multiply the two functions together. The given functions are:

- \( f(x) = 3x + 4 \)
- \( g(x) = x^2 - 2x \)

Now, the product \( (f \cdot g)(x) \) is calculated as:

\[
(f \cdot g)(x) = f(x) \cdot g(x)
\]
\[
= (3x + 4) \cdot (x^2 - 2x)
\]

Use the distributive property (FOIL method):

\[
= 3x(x^2 - 2x) + 4(x^2 - 2x)
\]
\[
= 3x^3 - 6x^2 + 4x^2 - 8x
\]
\[
= 3x^3 - 2x^2 - 8x
\]

Thus, the correct mathematical expression for \( (f \cdot g)(x) \) is:

\[
3x^3 - 2x^2 - 8x
\]

### The correct answer is: \( \mathbf{3x^3 - 2x^2 - 8x} \)

Would you like more details, or do you have any questions?

---

Here are 5 related questions for further practice:

1. What is the sum of \( f(x) \) and \( g(x) \)?
2. What is the composition \( (f \circ g)(x) \)?
3. Find the derivative of \( f(x) \cdot g(x) \).
4. What is the value of \( (f \cdot g)(2) \)?
5. Solve \( f(x) \cdot g(x) = 0 \).

**Tip**: When multiplying polynomials, always distribute each term in the first polynomial to each term in the second polynomial for accuracy.

The given two functions are f(x)=3x+4 and g(x)=x^2−2x. What mathematical expression would be for the product of the two functions (f∙g)(x)?

Learn how to find the product of the functions f(x)=3x+4 and g(x)=x^2−2x using the distributive property. This algebra problem covers polynomial multiplication and is suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation