https://r2.erweima.ai/mathbot/image/17265919131726ttu5yfo.jpg

It looks like you've uploaded an image of several mathematical functions. I will identify each function and provide you with solutions or relevant information as needed.

Here are the functions in the image:

1. **e)** \( f(x) = -2x^2 - 5 \)
2. **f)** \( f(x) = 2x^4 + x^2 - x^2 + 4 \) (This simplifies to \( f(x) = 2x^4 + 4 \))
3. **a)** \( f(x) = \frac{x^3 + 2}{3} \)
4. **h)** \( f(x) = \frac{1}{3x^2} \)
5. **i)** \( f(x) = \frac{x+1}{x-1} \)
6. **j)** \( f(x) = (5x^2 - 3)(x^2 + x + 4) \)
7. **k)** \( f(x) = (x^2 - 1)(x^3 + 3x) \)

Would you like to find the derivatives, integrals, or specific values for any of these functions? Let me know how you would like to proceed or if you'd like an explanation for any of these.

The user uploaded an image with several mathematical functions, including polynomial, rational, and factored forms. The user seeks to identify these functions and possibly solve for derivatives, integrals, or evaluate specific values.

Explore the solutions for polynomial and rational functions, including f(x) = -2x^2 - 5 and f(x) = (x^2 - 1)(x^3 + 3x). Learn the key concepts of algebra, factoring, and solving complex functions, suitable for high school students (Grades 10-12).

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