University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.1 - Functions and Their Graphs - Exercises - Page 12: 18


$\mathrm{Domain:}\ \ (-\infty ,0]$ $\mathrm{See\:the\:graph\:below.}$

Work Step by Step

We can take the square root only of positive numbers. Find the non-negative values of the radical by using: $\sqrt{f(x)}\quad \Rightarrow \quad \:f(x)\ge 0$ $-x\ge \:0$ Multiply both sides by -1 and reverse the inequality. $x\le \:0$ So, the function domain is, $\ (-\infty ,0].$ The graph of the given function $\ y=\sqrt{-x}\ $ is similar to the graph of the function $\ y=\sqrt{x}\ $, except that it is reflected over the $\mathrm{y-axis}.$ See the graph below.
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