Evaluate the function for f(x)=x+3 and g(x)=$$ x^2-2.\text{ (fg)}(6)\text{.} $$

To evaluate $(fg)(6)$, we need to first understand what $(fg)(x)$ represents. $(fg)(x)$ is the product of the two functions $f(x)$ and $g(x)$:

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

Given the functions:
- $f(x) = x + 3$
- $g(x) = x^2 - 2$

We now calculate $(fg)(6)$:

### Step 1: Calculate $f(6)$
\[
f(6) = 6 + 3 = 9
\]

### Step 2: Calculate $g(6)$
\[
g(6) = 6^2 - 2 = 36 - 2 = 34
\]

### Step 3: Multiply $f(6)$ and $g(6)$
\[
(fg)(6) = f(6) \cdot g(6) = 9 \cdot 34 = 306
\]

Thus, $(fg)(6) = 306$.

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

Here are 5 related questions:
1. What is $(fg)(x)$ for a different value, such as $x = 4$?
2. How would you evaluate $(f + g)(x)$ instead of $(fg)(x)$?
3. What happens if $f(x)$ and $g(x)$ are combined using division, like $(f/g)(x)$?
4. How do you find the domain of the product function $(fg)(x)$?
5. What would the result be if you differentiated $(fg)(x)$ with respect to $x$?

**Tip:** Always break down composite functions step-by-step to ensure accuracy in your calculations!

Evaluate the function for f(x)=x+3 and g(x)=x^2-2. (fg)(6).

Learn how to evaluate (fg)(6) for the functions f(x)=x+3 and g(x)=x^2-2. This algebra problem covers the multiplication of two functions and provides a step-by-step solution suitable for students in Grades 8-10.

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