Answer
The Domain of $h$ is $(-\infty,\infty)$ and $h$ is continuous in its domain.
Work Step by Step
\[h(x)=\cos (1-x^2)\]
Since domain of $\cos\theta$ is $(-\infty,\infty)$
$\Rightarrow$ domain of $h$ is continuous in $(-\infty,\infty)$
Since $\cos\theta$ is continuous for all real values of $\theta$ i.e, $(-\infty,\infty)$
$\Rightarrow $ $\cos (1-x^2)$ is continuous for all real values of $x$ i.e., $(-\infty,\infty)$
Which is domain of $h$
$\Rightarrow$ $h$ is continuous in its domain
Answer is: The Domain of $h$ is $(-\infty,\infty)$ and $h$ is continuous in its domain.
