For which type of functions is the inverse denoted as finverse{f(x)} = x?

The correct answer is invertible functions because these are the types of functions that have a well-defined inverse. An inverse function essentially "undoes" the action of the original function. If a function is invertible, it means that for every output value, there is a unique input value that produces it. This relationship can be expressed as finverse{f(x)} = x, indicating that applying the inverse function to the output of the original function returns the input.

For example, if you have a function f(x) that maps x to some value y, the inverse function finverse{f(x)} will take y back to x. This is true as long as the function is one-to-one (bijective), meaning that no two inputs map to the same output.

In contrast, functions that are not invertible do not satisfy this one-to-one requirement, which leads to ambiguous or multiple output values for a given input, making it impossible to define a proper inverse. Therefore, the defining characteristic of the correct answer is that the function's outputs correspond uniquely to its inputs, allowing for an inverse function to exist.