Final answer:
Performing a composition of inverses, such as a function and its inverse, results in the original input value (x) because each function 'undoes' the effect of the other, essentially producing the identity function.
Step-by-step explanation:
When you perform a composition of inverses, such as the composition of a function and its inverse (f(g(x)) or g(f(x))), the result is the original input value (x). This happens because the function and its inverse are designed to 'undo' each other. For example, if f(x) = 2x and its inverse f-1(x) = x/2, then composing these (f(f-1(x))) would yield (2(x/2)) = x, which returns the original input value. The same happens in reverse; (f-1(f(x))) would yield (1/2(2x)) = x.
Essentially, the composition of a function with its inverse will always produce the identity function on the domain of the original function. This is because the first function applies a certain 'transformation' to the input, and its inverse function applies the exact opposite 'transformation', thus cancelling out any changes and returning the input to its original state.