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Proposition: Compositions of Continuous Functions on a Whole Domain
Let \(f:D\to\mathbb R\) and \(g:E\to\mathbb R\) be real functions with \(f(D)\subseteq E\) such that \(f\) is continuous on \(D\) and \(g\) is continuous on \(f(D)\). Then their composition.
\[g\circ f:D\to\mathbb R\]
is continuous on \(D\).
Table of Contents
Proofs: 1
Mentioned in:
Corollaries: 1
Proofs: 2
Propositions: 3
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer VerĂ¤nderlichen", Vieweg Studium, 1983