Range of Tricky Tangent Function

Geometry Level 4

Find the range of the function

$\large f(x) = \dfrac{1 + \tan x}{1 - \tan x}.$

None of these

[0 , \infty)

(-\infty , -1]

(-\infty , \infty)

(-\infty , 1 ] \cup [1, \infty)

(-\infty , 0 ] \cup [0, \infty)

(-\infty , -1) \cup (-1, \infty)

(-\infty , 0]