The characterization of bijective functions motivates the following definition.

Definition: Invertible Functions, Inverse Functions

A function \(f:A\to B\) is called invertible, if there exists a function \(f^{-1}:B\to A\) such that $f^{-1}(y)=x$ if and only if $f(x)=y.$ If \(f\) is invertible, then \(f^{-1}\) is called the inverse function of \(f\).

Definitions: 1 2
Explanations: 3
Lemmas: 4
Proofs: 5 6 7 8 9 10
Propositions: 11 12 13 14

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  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983