8. Let

for x in the domain D = .

 

  1. Does f'(x) always have the same sign? Why? If so, is it positive or negative?

 

 

 

  1. Does f have an inverse function on D? Why or why not?

    2.  

     

    Since the function is always decreasing on its domain it has an inverse it is one to one, so has an inverse.

     

  2. Find , and then find

 

First

 

 

Then, letting g be the inverse of f:

 

Finally