Final answer:
The student's question involves writing formulas for functions that are composed of or operate on f(x), g(x), and h(x), then simplifying them. An example is given for f(g(x)), which simplifies to 2x - 5.
Step-by-step explanation:
The student is asking for a formula for the composition of the given functions and operations on these functions. Given that f(x) = 2x + 3, g(x) = x - 4, and h(x) = 2x² - 5x - 12, we can write new functions by plugging one function into the other (composition of functions) or by performing other operations as specified in the question. Without more specifics, we can demonstrate by a general example: if we want to compose f(g(x)), we would replace the 'x' in 'f' with 'g(x)', yielding f(g(x)) = 2(x - 4) + 3 = 2x - 8 + 3 = 2x - 5. A simplification process should follow each step to get the final form of the new function.