help (thanks in advance)

This is true, as the domain of arctan can accept any real number. the range however is limited to [-pi/2, pi/2] so it is continuous and 1-1 as a function.

The range does not include the two limit values  -pi/2  and  pi/2.

The range should be expressed as ( -pi/2, pi/2 )

using the round brackets to indicate that the endpoints are not included.