Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Section 1.1 - Real Numbers - 1.1 Exercises: 63


[0, 6]

Work Step by Step

When combining two sets of values for a variable, we must consider only its common portions. [-4, 6] U [0, 8) tells us that: *Note [ or ] represents inclusive *Note ( or ) represents exclusive, and is used for positive or negative infinite as well, as you cannot include the value of infinity, or even quantify it - The first set allows values from -4 to +6, inclusive - The second set allows values from 0 (inclusive) to 8 (exclusive) Both of these sets share a common portion, that is, a certain range of values. Since both include 0, that is the minimum value to specify. Moreover, the maximum value we can specify would be 6, as is the maximum value falling under both sets of numbers. Therefore, it can be written that the common set is 0 $\leq x \leq 6$, or [0, 6]
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