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 $(-\infty, \infty)$
