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# 6: Functions

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• 6.1: An Introduction to Functions
The functions we studied in calculus are real functions, which are defined over a set of real numbers, and the results they produce are also real. In this chapter, we shall study their generalization over other sets. The definition could be difficult to grasp at the beginning, so we would start with a brief introduction.
• 6.2: Deﬁnition of Functions
A function from A to B is a rule that assigns to every element of A a unique element in B .
• 6.3: One-to-One Functions
We distinguish two special families of functions: the one-to-one functions and the onto functions. We shall discuss one-to-one functions in this section.
• 6.4: Onto Functions
One-to-one functions focus on the elements in the domain. We do not want any two of them sharing a common image. Onto functions focus on the codomain. We want to know if it contains elements not associated with any element in the domain.
• 6.5: Properties of Functions
In this section, we will study some properties of functions.
• 6.6: Inverse Functions
• 6.7: Composite Functions