Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.8 Continuity - 1.8 Exercises - Page 92: 29

Answer

continuous on $(-\infty, \infty)$

Work Step by Step

Let g(x)=$-x^{2}+1$, , a polynomial, continuous everywhere, by theorem 5. Let f(x)$=\cos x$, continuous everywhere, by theorem 7. (polynomials, rational functions, root functions, trigonometric functions are continuous on their domains) $h(x)=f(g(x))$, a composite function of continuous functions, continuous on its domain, by Theorem 9. Its domain is $(-\infty, \infty)$
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