It looks like you've uploaded an image containing mathematical expressions and possibly some related questions. Let me extract and analyze the content for you.

Based on what I can discern from the text in the image, you have a function $g(x) = -2x^3 - 3x + 4$, and the values $g(1) = -1$, $g(0) = 4$, $f(1) = \frac{3}{2}$, and $f(0) = 1$ are given.

If you need to solve any specific problem related to these functions or need any explanations, please let me know! I can assist with calculations, verifying values, or working through any particular problem you're dealing with.

Would you like detailed explanations on how to work with these functions, or do you have specific questions related to them? Here are some possible directions:

1. Do you want to verify the values of $g(1)$ and $g(0)$ for the function $g(x)$?
2. Would you like to explore how the function $f(x)$ might be defined or calculated based on the given values $f(1)$ and $f(0)$?
3. Are you interested in finding the derivative of $g(x)$ or $f(x)$ to explore their slopes?
4. Would you like to solve for any points of intersection between $g(x)$ and $f(x)$ if such information is given or implied?
5. Do you need to sketch the graphs of these functions to better understand their behavior?

Tip: When dealing with polynomial functions like $g(x) = -2x^3 - 3x + 4$, calculating values at specific points can help in sketching the graph and understanding the function's general behavior.