[list][*]Function [math]f\left(x\right)=\left(x-2\right)^2-6[/math] is not one-to-one, but restricting its domain can yield a related function G which is one-to-one (and has an inverse function).[br][/*][*]Drag points X0 and X1 on x-axis to pick domain for one-to-one function G [plotted using black dashes].[br][/*][*]Green curve is reflection of black curve through the line y=x; it is the graph of inverse function [math]G^{-1}[/math] [named Ginv here].[/*][/list]

[list][*]Point P=(a,b) is on the graph of Ginv; you can move P.[br][/*][*]Point Q=(b,a) is mirror-image of P on graph of G.[br][/*][*]Tangent to G at Q is computed (using derivative of f at b) and displayed.[br][/*][*]Slope [math]f'\left(b\right)[/math] of tangent to G at Q is used to compute slope [math]\frac{1}{f'\left(b\right)}[/math] of tangent to [math]G^{-1}=Ginv[/math] at P.[br][/*][*]Knowing slope of tangent to Ginv at a (i.e., at point P) now lets the tangent to this inverse function to be displayed.[/*][*]Move P, see how that changes point Q and tangent there to G; also notice the two tangents (at Q and at P) meet at a point on the line y=x.[br][/*][*]Function f (and G) can be changed using the input box at bottom of the figure.[br][/*][/list]