This applet shows the inverse relation of a function.[br][br]The inverse of [math]y = f(x)[/math] is a relation [math]x = f^{-1}(y)[/math]. Graphically, the inverse relation is obtained by reflecting the graph of [math]y = f(x)[/math] about the line [math]y = x[/math].

Enter the rule for a function f(x) in the textbox at bottom-left. Click 'Show points' to display a point on the x-axis, and the point(s) corresponding to [math]f^{-1}(x)[/math]. Drag the blue point to change x.[br][br]What do you get as you drag x along the axis?[br][br]Click 'Show inverse' to display the entire inverse relation. Is it a function? You can click 'Vertical line test' to provide a vertical line which might help you decide.[br][br]Can you restrict the domain of [math]f[/math] to make the inverse a function?