Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - 2.1 Properties of Functions - 2.1 Exercises - Page 54: 22


$(-\infty, \infty)$

Work Step by Step

We want to determine all real $x$ values for which $f(x)=|3x-6|$ is defined. Starting inside the absolute values, we can always multiply any real number by 3 and then subtract 6 from the result, so $3x-6$ is defined for all real $x$. We can take the absolute value of any real number, so $|3x-6|$ is also defined for any real $x$. Thus, the domain of $f$ is all real numbers, written as $(-\infty,\infty)$ in interval notation.
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