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.