Domain and Range values of tan⁡x and tan^(-1)⁡x

Author:
Mathguru
We can clearly see two graphs one is in red color and the second one is in green color. Red graph is the locus of the function f(x)=tan⁡〖 (nx)〗 and the green graph is the locus of the function g(x)=tan^(-1)⁡〖 (nx)〗. We can change the value of n using the slide bar. We can also see 5 black points. These points are present on the tan x graph (red) with x-coordinates –π,-π/2,π/2,π,3π/2 . Let us change the values of n using the slide bar and see how the shape of the graphs change. Let us change the values of n and see how the shape, domain and range of the functions tan nx & tan^(-1)⁡nx get changed.
Questions to think about Let us find the values of the range and domain for the function tan⁡nx. Let us find the values of the range and domain for the function〖 tan〗^(-1)⁡nx. Let us observe how the values of the range and domain get changed when we change the values of tan nx & tan^(-1)⁡nx. Let us change the value of n and observe at which value along the x-axis we get the maximum and minimum values of the graph. What happens when n is a natural number.