Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - 2.3 Functions - 2.3 Exercises: 35

Answer

The given relation does not define $y$ as a function of $x$. domain: $[0, +\infty)$ range: $(-\infty, +\infty)$

Work Step by Step

For every positive value of $x$, the equation $x=y^6$ gives more than one value of $y$. Example: For $x=1$, the values of $y$ are $1$ and $-1$. This means that for some values of $x$, $x$ is paired with two values of $y$. Thus, the given relation does not define $y$ as a function of $x$. The value of $x$ can be any non-negative real number so the domain is $[0, +\infty)$. $y$ can be any real number. Thus, the range is $(-\infty, +\infty)$ .
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