Calculus 8th Edition

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