To find \((g + f)(n)\), we need to add the functions \(g(x)\) and \(f(x)\) and then substitute \(x = n\).

### Step 1: Add the functions \(g(x)\) and \(f(x)\)
Given:
- \(g(x) = 3x - 3\)
- \(f(x) = x^2 + 1\)

Now, add \(g(x)\) and \(f(x)\):
\[
(g + f)(x) = g(x) + f(x)
\]
\[
(g + f)(x) = (3x - 3) + (x^2 + 1)
\]
Simplifying:
\[
(g + f)(x) = x^2 + 3x - 3 + 1
\]
\[
(g + f)(x) = x^2 + 3x - 2
\]

### Step 2: Substitute \(x = n\)
Now, substitute \(n\) into \((g + f)(x)\):
\[
(g + f)(n) = n^2 + 3n - 2
\]

So, \((g + f)(n) = n^2 + 3n - 2\).

Would you like a detailed explanation on how I simplified the expression? 

Here are 5 questions related to this problem:
1. How do you find the sum of two functions in general?
2. What is the process of simplifying polynomials?
3. How do you find the value of a function at a specific point?
4. Can we subtract, multiply, or divide functions similarly?
5. What is function composition and how is it different from function addition?

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

Learn how to add the functions g(x) = 3x - 3 and f(x) = x^2 + 1, and find (g + f)(n). This problem covers algebraic concepts such as function addition and polynomial simplification. Suitable for students in Grades 8-10.

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