Continuity
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Inverse functions
Equations are omitted for technical reasons - download the original pdf
An inverse function only exists for functions that are one-to-one on a closed interval. In this context we need to be precise about the existence of an inverse function, so we prove an existence theorem for inverse functions. An inverse function of f exists if f is strictly increasing on a closed interval. Definition. Let [Equation goes here - download the original to see it.] be a closed interval, and suppose [Equation] for all [Equation] such that [Equation]. Then f is said to be increasing. If [Equation] then f is strictly increasing.
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Contents of
Continuity
1 Continuity
2 Properties of continuous functions
3 The intermediate value theorem
4 Bounds of continuous functions
5 A continuous function in a closed interval attains its bounds
6 Uniform continuity
7 Uniform continuity theorem
8 Inverse functions
9 Existence theorem for an inverse function
10 Maxima and minima
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