Inverse Functions
Author: Lenore Horner

In the window below you will be able to explore the idea of inverse functions.  The inverse of a function f is its reflection in the line y=x (shown below as the dashed blue line).  Below the window are more detailed instructions to guide your exploration.

Moving and zooming:
Find the crossed arrows (plus sign with arrows).  Click that to move around the graph.  Click the small triangle in the lower right corner of that icon to get further options: zooming.  If you are on a Mac, you can move by holding shift and dragging the mouse and you can zoom by holding shift and dragging the mouse along one of the axes.

Tracing the functions:
(Select the arrow tool at the left end of the tool bar.)
Click on point A (green diamond) and drag with the mouse to move it.  What happens when you move A?  How do the coordinates of A compare to the coordinates of the blue point.

Trying your own functions:
Double-click on f(x) in the left part of the window above.  Now you can type your own function in.  Does its inverse look the way you expected it to?  Try the following pairs of functions.  What do you notice about them?
f(x)=x/2+1  then f(x)=2x-2
f(x)=x^2  then f(x)=sqrt(x)
f(x)=ln(x)  then f(x)=e^x

e = 2.718281828459045
f(x) = e^(x)
A = Point(f)
Arefl = Mirror(A, m)
loc1 = Locus(Arefl, A)
a = Tangent(A, f)
b: y = 1.0 / f'(y(A)) * (x - x(Arefl)) + y(Arefl)