Question

Which equation represents a tangent function with a domain of all Real numbers such that x ≠ π + 2πn, where n is an integer?

Answer 1

Along the domain [0,2pi), the tangent function is not defined when x = pi/2 and x = 3pi/2.

Then, when we are considering the domain of all real numbers, tangent function is not defined for x = pi/2 + n*pi, where n is a integer.

We can check in the last option, j(x) = tan(x/2-pi), that when x = pi + 2*n*pi the argument would be -pi/2 + n*pi

Therefore, since the function is not defined at x = pi + 2*n*pi, the answer is: j(x) = tan(x/2-pi)