Homework # 8a:  Inverse Functions

Below are a few simple exercises that will help you understand better some of the basic ideas in Module 8.  You may use the Documentation Center to assist you with these problems.

Please format your solutions appropriately.  Use text format, not input format, when you are typing text.  Write coherent sentences and paragraphs;  part of your grade will depend on how clearly you present your ideas.

You must work on these exercises by yourself, not in pairs;  if you get stuck and cannot find the solution in the Documentation Center, you may consult the labbie or the instructor during their office hours.

Inverse Functions

1.  Explain in your own words the meaning of the term inverse function.

2.  What is the inverse function for each of the following functions: (Sqrt[x]), Log[x], (Sin^(-1))[x].  Use Mathematica to verify that in each case you have written the correct inverse function.

3.  Use Mathematica to find the inverse function to the function f[x]=((2x+3)/(4x-1)).  Then verify with Mathematica that your solution is correct.