“In mathematics, an inverse function (or anti-function) is a function that “reverses” another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa, i.e., f(x) = y if and only if g(y) = x. The inverse function of f is also denoted as 
“Not all functions have inverse functions. Those that do are called invertible. For a function f: X → Y to have an inverse, it must have the property that for every y in Y, there is exactly one x in X such that f(x) = y. This property ensures that a function g: Y → X exists with the necessary relationship with f.” In other words, f must be a bijection[1] to be invertible.
Notes:
- The inverse f −1, if it exists (and is two-sided), is unique.
- “While the notation f −1(x) might be misunderstood, (f(x))−1 certainly denotes the multiplicative inverse[2] of f(x) and has nothing to do with the inverse function of f.”
- “Even if a function f is not one-to-one, it may be possible to define a partial inverse of f by restricting the domain” https://en.wikipedia.org/wiki/Inverse_function#Partial_inverses
- “Left and right inverses are not necessarily the same.” https://en.wikipedia.org/wiki/Inverse_function#Left_and_right_inverses
Source: “Inverse Function,” Wikipedia, retrieved 11/7/2020, emphasis added.
- [1] What is the Gist of “Injective,” “Surjective,” and “Bijective” Functions (Mathematics)?
- [2] What is the Gist of “Invertibility” (Mathematics)?
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Disclaimer:
I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).