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Lemma: Invertible Functions on Real Intervals

Let \([a,b]\) be a closed real interval and let \(f:[a,b]\to\mathbb R\) be a continuous, strictly monotonically increasing (respectively decreasing) real function. Then \(f\) is invertible with the strictly monotonically increasing (respectively decreasing) inverse function \(f^{-1}:[A,B]\to[a,b]\). Therein, \(A\) and \(B\) are real numbers with \(A:=f(a)\) and \(B:=f(b)\).

Table of Contents

Proofs: 1

1. Proposition: Derivative of an Invertible Function on Real Invervals

Mentioned in:

Proofs: 1 2
Propositions: 3 4 5 6 7 8 9 10

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References

Bibliography

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