## Exploring Inverse Functions:  ln x Prof. Battaly, Calc 2, Westchester Community College

Examine the functions below, viewing both the graph and the algebra window, which provides both equations and values.
Begin by moving the a and b on the sliders in the upper left portion of the graph window. Click and drag the "a" or the "b". (For greater precision, click on the letter then use the arrow keys on your keyboard.)   You will be moving the tangent lines along the respective curves.
Note the changes in:  1)  the coordinates of the points A and B,   2) the equations of the tangent lines,   3) the slopes (e and h) of the tangent lines, and   4) the product of the slopes (eh).

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Are f(x) and g(x) inverse functions? Under what conditions? What evidence do you have to support your answer?
What can you say about the slopes of tangent lines for inverse functions?

G. Battaly, WCC, Created with GeoGebra              Related pages for Inverse Functions:  Class Notes, 5.3   Homework 5.3

Last Updated 02/02/09
By Prof. Battaly, http://www.battaly.com/
Email: merlin@pipeline.com