Trigonometric functions are not one-to-one. In order to have an inverse function for trigonometry, we restrict the domain of each function, so that it is one to one.
To have the inverse function, a tan function has to be restricted to the domain interval:
[tex]-\frac{\pi}{2}\text{ }to\text{ }\frac{\pi}{2}[/tex]
This is given to be:
[tex]-\frac{\pi}{2}Therefore,
the domain of f(x) = tan x is restricted to [tex]\Rightarrow(-\frac{\pi}{2},\frac{\pi}{2})[/tex]
Hence, the functional values of f(x) = arctan x are on the interval
[tex]\Rightarrow(-\frac{\pi}{2},\frac{\pi}{2})[/tex]
