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.