Skip to main content
Contents Index Dark Mode Prev Up Next \(\newcommand{\mylongdiv}[2]{#1\,\enclose{longdiv}{#2}}
\renewcommand{\emptyset}{\{\}}
\newcommand{\blanksp}{\underline{\hspace{.25in}}}
\newcommand{\eridfive}{\mathbf{\forall}}
\newcommand{\set}[1]{\left\{#1\right\}}
\newcommand{\cspace}{-}
\newcommand{\Ta}{\mathtt{a}}
\newcommand{\Tb}{\mathtt{b}}
\newcommand{\Tc}{\mathtt{c}}
\newcommand{\Td}{\mathtt{d}}
\newcommand{\Te}{\mathtt{e}}
\newcommand{\Tf}{\mathtt{f}}
\newcommand{\Tg}{\mathtt{g}}
\newcommand{\Th}{\mathtt{h}}
\newcommand{\Ti}{\mathtt{i}}
\newcommand{\Tj}{\mathtt{j}}
\newcommand{\Tk}{\mathtt{k}}
\newcommand{\Tl}{\mathtt{l}}
\newcommand{\Tm}{\mathtt{m}}
\newcommand{\Tn}{\mathtt{n}}
\newcommand{\To}{\mathtt{o}}
\newcommand{\Tp}{\mathtt{p}}
\newcommand{\Tq}{\mathtt{q}}
\newcommand{\Tr}{\mathtt{r}}
\newcommand{\Ts}{\mathtt{s}}
\newcommand{\Tt}{\mathtt{t}}
\newcommand{\Tu}{\mathtt{u}}
\newcommand{\Tv}{\mathtt{v}}
\newcommand{\Tw}{\mathtt{w}}
\newcommand{\Tx}{\mathtt{x}}
\newcommand{\Ty}{\mathtt{y}}
\newcommand{\Tz}{\mathtt{z}}
\newcommand{\So}{\Tf}
\newcommand{\Sno}{\Tg}
\newcommand{\Si}{\Th}
\newcommand{\Sni}{\Tj}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\W}{\mathbb{W}}
\newcommand{\ZZ}{\Z}
\newcommand{\PP}{\mathbb{P}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\RR}{\R}
\newcommand{\F}{\mathbb{F}}
\newcommand{\A}{\mathbb{A}}
\newcommand{\abs}[1]{|#1|}
\newcommand{\fmod}{\bmod}
\newcommand{\fdiv}{\,\mathrm{div}\,}
\newcommand{\lcm}{\mathrm{lcm}}
\newcommand{\id}{\mathrm{id}}
\newcommand{\nr}[1]{\##1}
\newcommand{\gexp}[3]{#1^{#2 #3}}
\newcommand{\gexpp}[3]{\displaystyle\left(#1\right)^{#2 #3}}
\newcommand{\glog}[3]{\log_{#1}^{#3}#2}
\newcommand{\sol}[1]{{\color{blue}\textit{#1}}}
\newcommand{\gro}[1]{{\color{gray}#1}}
\newcommand{\todo}[1]{{\color{purple}TO DO: #1}}
\newcommand{\fixme}[1]{{\color{red}FIX ME: #1}}
\newcommand{\checkme}[1]{{\color{green}CHECK ME: #1}}
\newcommand{\degre}{^\circ}
\newcommand{\vect}[1]{\overrightarrow{#1}}
\newcommand{\nix}{}
\newcommand{\cox}[1]{\fcolorbox[HTML]{000000}{#1}{\phantom{M}}}
\newcommand{\tox}[1]{\texttt{\##1} \amp \cox{#1}}
\newcommand{\ttx}[1]{\texttt{\##1}}
\newcommand{\mox}[1]{\mathtt{\##1}}
\newcommand{\xx}{\mathtt{\#}}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Chapter 7 Functions
Objectives
Demonstrate that two functions are equal.
Evaluate the composite of two functions.
Recognize the identity function on a set.
Recognize whether a function is invertible or not.
Demonstrate that a function is the inverse of another function.
Like sets, functions are a basic and important idea in mathematics. Functions help us work with numbers and other data. They also let us switch between different representations of objects.
This chapter introduces functions and their properties. We study some special functions, create new functions as composites of other functions, and study invertible functions. In later sections, we use invertible functions to switch between different representations of data.
