The range of $\sec^{-1}x$ (arcsecant) is $[0,\pi]\setminus\{\pi/2\}$, since $\sec(\pi/2)$ is undefined. The domain is $|x|\geq 1$ (i.e. $x\leq -1$ or $x\geq 1$), and the range is $[0,\pi]$ excluding the point $\pi/2$ where secant is undefined.