Final answer:
In mathematics, when two functions are inverses of each other, the composition of one with the other will result in the identity function, returning the original input x. It is the same regardless of the order of composition.
Step-by-step explanation:
The question appears to be about the composition of inverse functions in mathematics. When two functions are inverses of each other, the composition of one with the other will yield the identity function. This means that for functions f and g where g is the inverse of f, composing f(g(x)) or g(f(x)) will result in x. It will not matter which function is applied first; the result, after applying both functions in succession, will be the input x.
Here is an example: if f(x) = 2x + 3 and g(x) = (x - 3) / 2, then f and g are inverses of each other. The compositions f(g(x)) and g(f(x)) both simplify to x.
The concept that the composition of inverse functions results in the identity function is a fundamental one in algebra and function theory, and it is a crucial property used in many areas of mathematics, including calculus and higher-level math courses.