Visualize a function and its inverse relation. Note the point on the function (open dot) and point on the inverse relation (red) are related. Also, the tangent line for the point on the function graph is related to the tangent line on the inverse relation graph.

Grab the open dot to manipulate the "test" point on the function graph. Its counterpart on the inverse relation will move accordingly. Each dot actually "mirrors" the position of the other with respect to the y = x line.