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Let's first find \( (f + g)(x) \) using the given functions:

- \( f(x) = 3x^2 + 3x - 18 \)
- \( g(x) = x - 2 \)

The sum of the functions is:

\[
(f + g)(x) = f(x) + g(x) = (3x^2 + 3x - 18) + (x - 2)
\]

Now, let's combine like terms:

\[
(f + g)(x) = 3x^2 + 3x + x - 18 - 2
\]

\[
(f + g)(x) = 3x^2 + 4x - 20
\]

Therefore, the answer is:

\[
(f + g)(x) = 3x^2 + 4x - 20
\]

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Would you like to explore the other parts of the question, such as \( f - g \), \( fg \), or \( \frac{f}{g} \), or their domains?

Here are five related questions for you to consider:

1. What is \( (f - g)(x) \) for the given functions?
2. How do we find \( (fg)(x) \), the product of the two functions?
3. What are the restrictions on the domain when calculating \( \frac{f}{g}(x) \)?
4. How do you determine the domain of a sum of functions like \( f + g \)?
5. Can you solve \( f(x) = g(x) \) to find where the two functions intersect?

**Tip:** When adding or subtracting functions, always combine like terms carefully to simplify the expression.

Find f + g, f - g, fg and f/g. Determine the domain for each function. f(x) = 3x^2 + 3x - 18, g(x) = x - 2. What is (f + g)(x)? (Simplify your answer. Do not factor.)

Learn how to find the sum of two functions f(x) and g(x) for f(x) = 3x^2 + 3x - 18 and g(x) = x - 2. This problem demonstrates polynomial addition and combining like terms. Suitable for students in Grades 9-12.

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