Answer
(a) $\tan^{-1}{2}$ is defined.
(b) $\cos^{-1}{2}$ is undefined
Work Step by Step
a) The domain of arctan includes all real numbers, so $\tan^{-1}{2}$ is defined.
b) The domain of arccos lies between -1 and 1, but the value 2 does not lie in that interval, so $\cos^{-1}{2}$ is not defined.
