Exercises

1. Enter each function below, then do parts A through D.
   
   $$f(x)=\frac{x}{x^2+1}$$
   
   
   
   
   $$g(x)=x^{\frac{3}{5}}$$
   
   
   
   
   $$h(x)=\frac{\ln(x-2)}{x}$$
   
   
   
   
   $$j(x)=\frac{(x+5)^3}{24}+4$$
   
   
   1. Plot each function over a range that gives a good representation of the function. Which functions are not invertible and why?
   2. Find the inverses of the invertible functions.
   3. First enter the command:

      >with(RealDomain):
      

      Plot each invertible function and its inverse along with the line $y=x$.Again use a domain and range that shows they are inverses.
   4. Show that you have the correct inverse by using the composite definition for each invertible function.