Section 7.2 Worksheet:

Assigned problems: Exercises pp. 356-358, 1-7, 17, 18, 28, 30, 43, 44

  1. What is a one-to-one function, and how can you spot it at a glance?

  2. How is the horizontal line test related to the vertical line test?

  3. How is the graph of tex2html_wrap_inline204 obtained from the graph of f?

  4. How is the derivative of the inverse tex2html_wrap_inline204 function related to that of the function f itself? Does this make sense graphically?

  5. Example #4, page 354 gives us an example of what to do when we need an inverse function of a function which is non-invertible. This suggests how we might create an inverse function for important functions like tex2html_wrap_inline212 and tex2html_wrap_inline214 . How so?

Notes:

  1. There is a terrible risk of confusion when it comes to the notation for inverse functions. We denote the inverse of f as tex2html_wrap_inline204 , but historically this means ``f to the negative one power,'' and so students believe that tex2html_wrap_inline204 means tex2html_wrap_inline224 : this is incorrect! Be careful to distinguish between these two cases.



Tue Nov 20 01:36:34 EST 2007