https://file.aiquickdraw.com/mathbot/file/1728050890851d7pg8rhs.jpg

Let's solve each of these problems step by step:

### Question 3:

**Given:**
- \( f(x) = x^3 \)
- \( g(x) = 2x - 5 \)
- We need to find \( (f + g)(x) \).

The function \( (f + g)(x) \) is defined as:
\[
(f + g)(x) = f(x) + g(x)
\]
Substitute the given functions:
\[
(f + g)(x) = x^3 + (2x - 5)
\]
Simplify:
\[
(f + g)(x) = x^3 + 2x - 5
\]

The correct answer is **A. \( x^3 + 2x - 5 \)**.

---

### Question 4:

**Given:**
- \( f(x) = 2x + 4 \)
- \( g(x) = x^2 - 3 \)
- We need to find \( (f + g)(x) \).

The function \( (f + g)(x) \) is defined as:
\[
(f + g)(x) = f(x) + g(x)
\]
Substitute the given functions:
\[
(f + g)(x) = (2x + 4) + (x^2 - 3)
\]
Simplify:
\[
(f + g)(x) = x^2 + 2x + 1
\]

The correct answer is **B. \( x^2 + 2x + 1 \)**.

---

Let me know if you want more details or have any other questions!

### Follow-up Questions:
1. How do you handle subtraction in similar problems?
2. Can \( f(x) \) and \( g(x) \) be more complex functions (like involving trigonometric terms)?
3. What happens if you're asked to find \( (f - g)(x) \)?
4. How would you verify the correctness of the solutions for similar problems?
5. Can you find \( (f \cdot g)(x) \) for these functions?

**Tip:** Always simplify your results by combining like terms carefully to avoid common errors.

If f(x) = x^3 and g(x) = 2x - 5, what is (f + g)(x)?
For f(x) = 2x + 4 and g(x) = x^2 - 3, what is (f + g)(x)?

Solve function addition problems where f(x) = x^3 and g(x) = 2x - 5. Also, explore adding quadratic and linear functions, such as f(x) = 2x + 4 and g(x) = x^2 - 3, and simplify the result step by step. Suitable for students in Grades 9-10.

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