Given the linear functions f(x) = x − 2 and g(x) = −3x + 4, determine (f ⋅ g)(x).

 (f ⋅ g)(x) = −3x − 8
 (f ⋅ g)(x) = −3x2 − 8
 (f ⋅ g)(x) = −3x2 + 10x − 8
 (f ⋅ g)(x) = −3x2 − 2x − 8

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

1. Given: 
   - \(f(x) = x - 2\)
   - \(g(x) = -3x + 4\)

2. Multiply \(f(x)\) by \(g(x)\):

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

Now expand the product:

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

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

Combine like terms:

\[
-3x^2 + 10x - 8
\]

Thus, \((f \cdot g)(x) = -3x^2 + 10x - 8\).

The correct option is:

\[
\boxed{(f \cdot g)(x) = -3x^2 + 10x - 8}
\]

Would you like a detailed explanation of any step?

### Related questions:
1. What is the domain of \((f \cdot g)(x)\)?
2. How do you find the sum \(f(x) + g(x)\)?
3. What would the graph of \((f \cdot g)(x)\) look like?
4. How do you determine the zeros of \((f \cdot g)(x)\)?
5. How would you solve \((f \cdot g)(x) = 0\)?

#### Tip:
When multiplying two functions, remember to apply the distributive property carefully to avoid errors in combining terms.

Given the linear functions f(x) = x − 2 and g(x) = −3x + 4, determine (f ⋅ g)(x).

(f ⋅ g)(x) = −3x − 8
(f ⋅ g)(x) = −3x^2 − 8
(f ⋅ g)(x) = −3x^2 + 10x − 8
(f ⋅ g)(x) = −3x^2 − 2x − 8

Learn how to multiply two linear functions, f(x) = x − 2 and g(x) = −3x + 4, to determine (f ⋅ g)(x). This algebra problem involves polynomial multiplication using the distributive property. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation