Final answer:
The question relates to finding functions g(x) and h(x) based on a given function f(x), but specific information about f(x) is missing. To answer, the explicit form of f(x) and the operations to derive g(x) and h(x) are needed.
Step-by-step explanation:
From the information provided, it appears that the student is asking a mathematics question related to functions. However, the specific functions g(x) and h(x) the student is asked to find are not clearly given in the details provided.
To assist the student, it would be necessary to have the explicit form of f(x) as well as the operations or transformations needed to derive g(x) and h(x). The references to displacements and probabilities suggest a variety of mathematical topics, such as vector addition and probability distributions, which are also relevant and common in a high school level mathematics class.
The concepts of vector addition and finding probabilities are very broad, so without further details on f(x), definitive solutions for g(x) and h(x) cannot be provided. If the student can provide the form of f(x), then we can proceed to find g(x) and h(x) using appropriate mathematical operations.
To find g(x) and h(x) given f(x), we need more information about the functions. Please provide the specific definitions of g(x) and h(x) or any additional details that will allow us to determine their relationship to f(x).