This applet can be used to study inverse functions.[br][list][*]Enter a function of [math]x[/math] in the input box.[br][/*][*]Set the domain of the function by dragging the arrows at the ends of the blue segment at the bottom of the window.[br][/*][*]Click on the “Horizontal Line Test” and drag the vertical slider. Is [math]f\left(x\right)[/math] a one-to-one function?[br][/*][*]Click on the “Reflect f(x)” button to reflect the graph of [math]f\left(x\right)[/math] about the line [math]y=x[/math].[/*][*]Drag the horizontal slider to run the Vertical Line Test. Is the reflection of the graph of [math]f\left(x\right)[/math] a graph of a function?[br][/*][*]Drag the arrows at the ends of the blue segment under the graphs to restrict the domain of [math]f\left(x\right)[/math] in such a way that the reflected graph is a graph of a function.[br][/*][*]Click the “Show Corresponding Points”. Drag the orange point along the graph of [math]f\left(x\right)[/math]and notice its reflection on the graph of the inverse function [math]f^{-1}\left(x\right)[/math].[/*][/list]