Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 3 - Review - Exercises - Page 322: 102

Answer

(0, 1)

Work Step by Step

The question asks for the domain of the function given in the problem Given $f(x) = \frac {1}{\sqrt[4] {x - x^4}} > 0$ The domain is such that $x - x^4$ is greater than 0. $x - x^4 > 0$ $x (1 - x^3) > 0$ $x (1 - x) (1 + x + x^2) \leq 0$ $x = 0, 1$ (-∞, 0) $\frac{(+)}{(-)(-)(+)} = (+)$ (0, 1) $\frac{(+)}{(+)(-)(+)} = (-)$ (1, ∞) $\frac{(+)}{(+)(+)(+)} = (+)$ Thus the Domain is (0, 1)
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