write short answers.\nconsider the inverse tangent function, defined by ( y = \tan^{-1}x ), or ( y = arctan…

write short answers.\nconsider the inverse tangent function, defined by ( y = \tan^{-1}x ), or ( y = arctan x ). complete parts (a)-(d).\n(a) what is its domain?\n(type your answer in interval notation. simplify your answer. type an exact answer, using ( pi ) as needed. use integers or fractions for any numbers in the expression.)

write short answers.\nconsider the inverse tangent function, defined by ( y = \tan^{-1}x ), or ( y = arctan x ). complete parts (a)-(d).\n(a) what is its domain?\n(type your answer in interval notation. simplify your answer. type an exact answer, using ( pi ) as needed. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Recall the definition of the inverse tangent function

The inverse tangent function (y = \tan^{-1}x) or (y=\arctan x) is defined as the inverse of the tangent function (y = \tan x) restricted to the interval (\left(-\frac{\pi}{2},\frac{\pi}{2}\right)). For a function (y = f(x)) and its inverse (x = f^{-1}(y)), the domain of (f^{-1}) is the range of (f). The range of the tangent function (y=\tan x) for (x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)) is ((-\infty,\infty)).

Answer:

((-\infty,\infty))