We are given two functions:

• $f(x) = 3x^2 + 2$
• $g(x) = 2x^2 - 3$

We are asked to find $(f + g)(x)$, which is the sum of the two functions. This can be written as:

$(f + g)(x) = f(x) + g(x)$

Now, substituting the expressions for $f(x)$ and $g(x)$:

$(f + g)(x) = (3x^2 + 2) + (2x^2 - 3)$

Simplifying the expression:

$(f + g)(x) = 3x^2 + 2x^2 + 2 - 3$ $(f + g)(x) = 5x^2 - 1$

So, the result is:

$(f + g)(x) = 5x^2 - 1$

Let me know if you have any questions or if you'd like further details.

Here are 5 related questions:

1. What is the general rule for adding two functions?
2. How would you find $(f - g)(x)$ instead of $(f + g)(x)$?
3. How do you perform function multiplication, for example $(f \cdot g)(x)$?
4. Can you apply the same steps to combine more than two functions?
5. How does the result change when $f(x)$ and $g(x)$ involve terms of different powers?

Tip: When adding or subtracting functions, always combine like terms (terms with the same powers of $x$).