The exercise is to graph this function below.
$$y = \arctan\left(\frac{e^x-1}{\sqrt3}\right)-\arctan\left(\frac{e^x-4}{\sqrt3e^x}\right)$$
If the exercise were just one trigonometric function, then I would just put the expression inside arctangent in argtangent's domain and moreover put $y$ in the range of which the argtangent is defined. However there are two trigonometric functions in the equation above, and I do not know where I would start to able to sketch it.
I also want to add that I solved the equation algebraically by taking the tangent of both sides and using the subtaction of two angle for tangent
$$ \tan(x-y)=\frac{\tan\ x + \tan\ y}{1 + \tan\ x*\tan\ y}$$
The equation simplified to $\tan\ y = \sqrt3$, which gives us $y = \frac{\pi}{3}$. Does this $y$ value help me sketch the function in anyway?