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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 \( x \)).

f(x) = 3x^2 + 2, g(x) = 2x^2 - 3. Find (f + g)(x).

Learn how to find the sum of two quadratic functions, f(x) = 3x^2 + 2 and g(x) = 2x^2 - 3, with a detailed step-by-step solution. This example explains function addition and simplifying quadratic expressions, suitable for students in Grades 9-11.

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