A function converts an [math]x[/math] value to a [math]y[/math] value so the inverse operation would take a [math]y[/math] value back to the original [math]x[/math] value. Because the inverse operation would take a [math]y[/math] value to an [math]x[/math] value the axis and names are switched. The inverse operation of a function can be shown on a graph by reflecting the function about the line [math]x=y[/math] which is equivalent to switching the [math]x[/math] and [math]y[/math] axes.[br]The inverse of a function [math]f(x)[/math] is labeled as [math]f^{-1}(x)[/math]. However, not all functions have inverse functions. You can enter a function in the entry box. This applet will then tell whether the inverse operation is a function. This test is performed only on the visible portion of the domain of the inverse operation.[br]Checking the "Path" checkbox will show the path of numbers. By moving the initial x value ( the orange plus ) it can be seen that [math]f^{-1}(f(x))=x[/math] if [math]f^{-1}[/math] is a function. Also, from exchange of functions [math]f(f^{-1}(x))=x[/math][br][br]

[br][br]Determine what requirement must the original function satisfy in order to have an inverse function.[br]Also, note the Domain and Range of the function and inverse operation.[br][br]Is there a way to limit the domain or range of the flipped function so that it could be a function.