Answer:
Step-by-step explanation:
First look at the tangent function f(x) = tan x. Its domain is restricted: (-pi/2, pi/2). There are no restrictions on the function value, so the range is (-infinity, +infinity). The primary interval on which tan x is defined is (-pi/2, +pi/2, which has length pi.
In comparison, the domain of f(x) = tan 2x is only half as long as that of f(x) = tan x: (-pi/4, +pi/4), with length pi/2.
Now, focusing on f(x) = 3cot(2x): the range is the same: (-infinity, +infinity). The period is half that of tan x: pi/2 instead of pi. Remember that the cotangent function repeats itself every pi/2 radians.
Domain: (-pi/4, +pi/4) (centered on the origin), (-3pi/4. 3pi/4), and so on, continuing to both the left and the right.
Range: (-infinity, infinity)
