Answer
domain: $x\in\mathbb{R} \text{ except } x=\frac{(2k+1)\pi}{2}$ (odd integer multiples of $\frac{\pi}{2}$)
range: $(-\infty,-1]\cup[1,\infty)$
Work Step by Step
By definition the domain is any real number except $x=\frac{(2k+1)\pi}{2}$, where $k$ is an integer (because $\sec x=\frac{1}{\cos x}$ and $\cos x$ is undefined there), whilst the range is $(-\infty,-1]\cup[1,\infty).$
