Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.1 - Functions - Exercises - Page 157: 63

Answer

$D=\{x|x\leq\dfrac{1}{2}\}=(-\infty,\dfrac{1}{2}]$

Work Step by Step

$f(x)=\sqrt{1-2x}$ This function is undefined when the expression inside the root is a negative number. To find the domain, let's solve the following inequality: $1-2x\geq0$ $2x\leq1$ $x\leq\dfrac{1}{2}$ All the numbers less than $\dfrac{1}{2}$, including it, are part of the domain of the function. This can be expressed as follows: $D=\{x|x\leq\dfrac{1}{2}\}=(-\infty,\dfrac{1}{2}]$
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