https://file.aiquickdraw.com/mathbot/file/1730830750597yvd7uwzq.jpg

To solve for \((f \cdot g)(x)\) when \(f(x) = x + 2\) and \(g(x) = x^2 + 4x + 4\), we need to calculate the product of \(f(x)\) and \(g(x)\), which is defined as:

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

### Step-by-Step Solution

1. **Write down \(f(x)\) and \(g(x)\):**
   - \(f(x) = x + 2\)
   - \(g(x) = x^2 + 4x + 4\)

2. **Multiply \(f(x)\) and \(g(x)\):**
   \[
(f \cdot g)(x) = (x + 2)(x^2 + 4x + 4)
   \]

3. **Expand the expression:**
   - Distribute \(x\) through \((x^2 + 4x + 4)\):
     \[
     x \cdot (x^2 + 4x + 4) = x^3 + 4x^2 + 4x
     \]
   - Distribute \(2\) through \((x^2

Find \((f \cdot g)(x)\) if \(f(x) = x + 2\) and \(g(x) = x^2 + 4x + 4\).

Learn how to find the product of two functions, (f \cdot g)(x), where f(x) = x + 2 and g(x) = x^2 + 4x + 4. This solution covers polynomial multiplication and expansion, suitable for high school students in grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation