https://file.aiquickdraw.com/mathbot/file/1726508491381hv39j5us.jpg

The image contains three functions:

1. \( f(x) = \sqrt{x^2 + 2} \)
2. \( g(x) = (3x + 1)^3 \)
3. \( h(x) = \frac{1}{(x^4 + 3)^2} \)

Would you like me to analyze any particular aspect of these functions (e.g., their derivatives, integrals, or domain/range)? Let me know how you'd like to proceed!

Here are some related questions:
1. What is the derivative of \( f(x) = \sqrt{x^2 + 2} \)?
2. What is the derivative of \( g(x) = (3x + 1)^3 \)?
3. What is the domain of the function \( h(x) = \frac{1}{(x^4 + 3)^2} \)?
4. How do you find the local maxima or minima of these functions?
5. Can we analyze the concavity of \( f(x) \) and \( g(x) \)?

**Tip:** To calculate the domain of a function, start by checking if the expression under square roots and in denominators is valid for all real numbers.

f(x) = √(x^2 + 2), g(x) = (3x + 1)^3, et h(x) = 1 / (x^4 + 3)^2

Explore the functions f(x) = √(x^2 + 2), g(x) = (3x + 1)^3, and h(x) = 1 / (x^4 + 3)^2. This page provides a deep dive into algebraic manipulations, their derivatives, and their applications in higher-level math. Ideal for undergraduate students.

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