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The problem provided asks to find \((f + g)(x)\), given the following functions:

- \( f(x) = 2x^3 - 5x + 4 \)
- \( g(x) = 3x^2 + 2x - 6 \)

To find \((f + g)(x)\), we simply add the two functions together:

\[
(f + g)(x) = f(x) + g(x)
\]

Substitute the expressions for \(f(x)\) and \(g(x)\):

\[
(f + g)(x) = (2x^3 - 5x + 4) + (3x^2 + 2x - 6)
\]

Now, combine like terms:

\[
(f + g)(x) = 2x^3 + 3x^2 - 5x + 2x + 4 - 6
\]

Simplify the terms:

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

So, \((f + g)(x)\) is:

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

Would you like more details on this? 

Here are 5 related questions:
1. How would you subtract \(g(x)\) from \(f(x)\)?
2. What is \((f \cdot g)(x)\) for the given functions?
3. How do you find the derivative of \((f + g)(x)\)?
4. Can you evaluate \((f + g)(x)\) for a specific value of \(x\)?
5. What is the degree of the polynomial \((f + g)(x)\)?

**Tip**: When adding polynomials, always combine like terms carefully to avoid mistakes in simplification.

Let f(x) = 2x^3 - 5x + 4 and g(x) = 3x^2 + 2x - 6. Find (f + g)(x).

Learn how to add two polynomial functions f(x) = 2x^3 - 5x + 4 and g(x) = 3x^2 + 2x - 6 by combining like terms. This problem involves basic algebraic concepts such as polynomial addition and simplification, suitable for Grades 10-12.

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