# hw5ANSWERS - \documentclass[12pt]cfw_article \textwidth =...

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\documentclass[12pt]{article} \textwidth = 6.5 in \textheight = 9 in \oddsidemargin = 0.0 in \evensidemargin = 0.0 in \topmargin = 0.2 in \headheight = 0.0 in \headsep = 0.0 in \parskip = 0.2in \parindent = 0.0in \usepackage{amsmath,amssymb,enumerate} %\def\rmdefault{bch} % Use Charter for main text font. % ========================================================= \begin{document} Neal Whittington (whittin3) Tuesdays, at 4:00PM AD9 \begin{center} {\LARGE \textbf{CS 173: Discrete Structures, Spring 2010} \\ \textbf{Homework 5} \\[1ex]} This homework contains 5 problems worth a total of 50 regular points, plus three bonus points. It is due on Friday, March 5th at 4pm. \end{center} \begin{enumerate} %---------------------------------------------------------------------- \item \textbf{Functions [8 points]} For each of the following functions, give the following information: what is its co-domain? what is its image? is the function onto? is the function one-to-one? \begin{enumerate} \item $f: \mathbb{Z} \rightarrow \mathbb{Z}$ such that $f(x) = 2 \lfloor \frac{x}{2} \rfloor$ \\Co-domain: $\mathbb{Z}$ \\Image: $\{2 \lfloor \frac{x}{2} \rfloor | x \in \mathbb{Z} \}$ \\Onto?: No \\One-to-one?: Yes \item $g: \mathbb{N} \rightarrow \mathbb{N}$ such that $g(x) = \frac{x(x+1)}{2}$ \\Co-domain: $\mathbb{N}$ \\Image: $\{\frac{x(x+1)}{2} | x \in \mathbb{N} \}$ \\Onto?: No \\One-to-one?:Yes \item $h: \mathbb{C} \rightarrow \mathbb{R}$ such that $h(ai + b) = a$ (where $i = \sqrt{-1}$) \\Co-domain: $\mathbb{R}$ \\Image: $\mathbb{R}$ \\Onto?: Yes \\One-to-one?: No \item $k: \mathbb{R}^2 - \{(0,0)\} \rightarrow \mathbb{R}^2$ such that $k(x,y) = (\frac{x}{l(x,y)}, \frac{y}{l(x,y)})$ where

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## hw5ANSWERS - \documentclass[12pt]cfw_article \textwidth =...

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