Question

In the study of logarithns and exponentials we first learn about one-to-one functions and inverse functions because the logarithm and exonential functions are inverse functions. Many conceptsare involved in the study of these two topics. Please demonstrate your understanding of the concepts by following the discussion guideline below:

Start with a medium difficulty level function and then find its inverse function (should take at least 3 steps) and write the inverse function in terms of x.  Name the original function f(x) and its inverse function g(x) and then show they are inverses by using composition functions.  

That is, show that f(g(x))= x and that g(f(x)) = x.

• If this was for a required grade the Grading Rubric would be like this:
  • 2 points Define a medium level function, f(x).
  • 2 points Determine and write the inverse function, f^-1(x). Then rename it g(x) to finish the problem.
  • 2 points Perform the composite function f(g(x)) to get the result of x.
  • 2 points Perform the composite function g(f(x)) to get the result of x.
  • 1 point Based upon your findings, state if f(x) and g(x) are inverse functions.
  • 1 point Explain why f(x) and g(x) are inverses or why they are not

Answer 1