Explore the graphical and numerical relationship between a function and its inverse.
Enter any function for f(x). Move the slider between f(x) and f-inverse(x) to view the graph flipping over the line y = x. Toggle the checkboxes in order to hide/show either curve. When the inverse is displayed, slide point A along the graph of f(x), observing how its coordinates relate to the coordinates of point B (which slides along the f-inverse(x) curve). Depending on your choice for f, notice that f-inverse sometimes is a function, and sometimes it is not. What must be true about f in order for f-inverse to be a function? When the inverse is not a function, adjust the ymin and ymax sliders to restrict its range and force it to become a function. Enter different choices for f(x). Alternately, you may drag the current f(x) curve to a new position on the x-y plane (exhibiting "translation"). Depending on how you change the function, points A and B may disappear off the screen. The x-value of point A stays fixed as you change the function, so strategically positioning point A before you change the function may help you keep the points in view.