Abstract
Let I be an interval in ℝ, let f be a function I → ℝ, and let J = f(I). If f(x) = f(x′) ⇒ x = x′, then f is invertible. If so, there is function f-1: J → I such that for each x ∈ I, f-1 (f(x)) = x, and for each y ∈ J, f(f-1(y)) = y. (To be precise, f-1 = {(y,x)|(x,y) ∈ f}.) f-1 is called the inverse of f.
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© 1982 Springer-Verlag New York, Inc.
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Moise, E.E. (1982). Invertible Functions. Arc-length and Path-length. In: Introductory Problem Courses in Analysis and Topology. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8183-9_8
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DOI: https://doi.org/10.1007/978-1-4613-8183-9_8
Publisher Name: Springer, New York, NY
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