Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
[ "article:topic-guide", "authorname:hkwong", "license:ccbyncsa", "showtoc:yes" ]
Mathematics LibreTexts

6: Functions

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    • 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