Final answer:
F(x), g(x), and h(x) represent different functions, each with their distinct relations between input and output. In linear equations, variables and their dimensions are consistent, and operations involving these functions and derivatives maintain that consistency.
Step-by-step explanation:
The notation f(x), g(x), and h(x) represent different functions. Each function is a distinct relation that assigns exactly one output for each input. The variables x and y often represent the input and output of a function, respectively. In mathematics, it is essential that every term in an expression has the same dimensions, and functions allow us to model relationships between quantities with consistent dimensions. For example, in linear equations like y = mx + b, x and y are variables representing the input and output, while m represents the slope and b the y-intercept of the graph of the function, respectively. The dimensions of mathematical operations or derivatives are also important, as they must be consistent with the quantities involved.