Final answer:
To check if two equations are inverses, compose the functions by substituting one into the other. If the composition yields the identity function for all elements in their domains, they are inverses. This involves solving compositions such as f(g(x)) and g(f(x)) and verifying if they equal x.
Step-by-step explanation:
When you want to find whether two equations are inverses of each other, you need to perform the composition of the two functions. This process is achieved by substituting one function into the other. Specifically, if you have two functions, f(x) and g(x), you will calculate both f(g(x)) and g(f(x)).
If the result of f(g(x)) is x for every element in the domain of g, and the result of g(f(x)) is x for every element in the domain of f, then the two functions are indeed inverses of each other. This also means that the composition of the functions should yield the identity function, i.e., I(x) = x. Remember that in order to be true inverses, this condition must hold true for all elements within the domain of these functions.
In practice, you would:
- Identify the unknown function's output.
- Identify the known function's input.
- Compose the functions by plugging in the knowns into the inverse equation and solve for the unknown.