Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 0 - Before Calculus - 0.1 Functions - Exercises Set 0.1: 4

Answer

(a) f(x) -> {x : x $\ne$ -1} = (-$\infty$, -1) U (-1, +$\infty$) g(x) -> (-$\infty$, +$\infty$) (b) f(x) -> {x : x $\geq$ 0} = [0, +$\infty$) g(x) -> {x : x $\geq$ 0} = [0, +$\infty$}

Work Step by Step

(a) The denominator, in f(x), must be $\ne$ 0, so x $\ne$ -1. There are no restrictions for x in g(x). (b) If x $\geq$ 0 the denominator never vanishes. It's only necessary to know that $\sqrt x$ is valid for every x $\geq$ 0.
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