Evaluate the function for 

f(x) = x + 3

 and 

g(x) = x2 − 2.

(fg)(8)

To solve \((fg)(8)\), we need to first understand that the function \( (fg)(x) \) is the product of \( f(x) \) and \( g(x) \), which can be written as:

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

### Step 1: Evaluate \( f(8) \)

Given:
\[
f(x) = x + 3
\]

Substitute \( x = 8 \) into \( f(x) \):
\[
f(8) = 8 + 3 = 11
\]

### Step 2: Evaluate \( g(8) \)

Given:
\[
g(x) = x^2 - 2
\]

Substitute \( x = 8 \) into \( g(x) \):
\[
g(8) = 8^2 - 2 = 64 - 2 = 62
\]

### Step 3: Multiply the results

Now, multiply \( f(8) \) and \( g(8) \):
\[
(fg)(8) = f(8) \cdot g(8) = 11 \cdot 62 = 682
\]

Thus, \((fg)(8) = 682\).

Would you like further details on function multiplication or any other concept?

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Here are some related questions:
1. What is the general form of \( (fg)(x) \)?
2. How do you evaluate \( (f+g)(x) \) for specific values of \( x \)?
3. What is the difference between function composition and function multiplication?
4. How would you solve \( (f/g)(x) \) for \( f(x) = x + 3 \) and \( g(x) = x^2 - 2 \)?
5. Can you solve \( (fg)(-2) \) for the same functions?

**Tip:** Always evaluate individual function values before performing operations like multiplication or division.

Evaluate the function for f(x) = x + 3 and g(x) = x^2 − 2. (fg)(8)

Learn how to evaluate the product of functions (fg)(8) where f(x) = x + 3 and g(x) = x^2 − 2. This step-by-step guide explains how to calculate the value of f(8), g(8), and their product. Suitable for students in Grades 9-10.

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