College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Chapter 4 Review - Concept Check - Page 425: 18


Domain: $-1\lt x\lt2$

Work Step by Step

We must have that: $2+x-x^2\gt0$ $2+2x-x-x^2\gt0$ $2(1+x)-x(1+x)\gt0$ $(2-x)(1+x)\gt0$ Both factors must be positive: $2-x\gt0$ $-x\gt-2$ $x\lt2$ $1+x\gt0$ $x\gt-1$ $-1\lt x\lt2$ Or both factors must be negative: $2-x\lt0$ $-x\lt-2$ $x\gt2$ $1+x\lt0$ $x\lt-1$ A number can not be greater than 2 and less than -1 at the same time.
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