Answer
Domain: All real numbers such that $ t \ne 2 + 4k $ , where $k$ is an integer
Range: $ (-\infty, -1] \cup [1,\infty) $
Work Step by Step
Secant functions are not defined at $ \frac{\pi}{2}+\pi k $ , where $k$ is an integer. So $ \sec{\frac{\pi t}{4}} $ is not defined at:
$ \frac{\pi t}{4} = \frac{\pi}{2}+\pi k $
$ t = (\frac{\pi}{2}+\pi k) \frac{4}{\pi} $
$ t = 2 + 4k $
The range of a secant function is $ (-\infty, -1] \cup [1,\infty) $.
