The restriction that should be applied to the function [tex]y = tanx[/tex] for [tex]tan^{-1} (x)[/tex] to be defined is option (C) restrict the domain to [tex](-\frac{\pi }{2} ,\frac{\pi }{2} )[/tex] is the correct answer.
What is graph of a function?
A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).
For the given situation,
The graph below shows the functions tan(x) and arctan(x) that is tan^-1(x)
In order to have an inverse function for trigonometry, we restrict the domain of each function, so that it is one to one.
A restricted domain gives an inverse function because the graph is one to one and able to pass the horizontal line test.
Thus by restricting the domain [tex](-\frac{\pi }{2} ,\frac{\pi }{2} )[/tex] we can obtain the function [tex]tan(x)[/tex] as [tex]tan^{-1} (x)[/tex].
Hence we can conclude that the restriction that should be applied to the function [tex]y = tanx[/tex] for [tex]tan^{-1} (x)[/tex] to be defined is option (C) restrict the domain to [tex](-\frac{\pi }{2} ,\frac{\pi }{2} )[/tex] is the correct answer.
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