composition and transformation of functions

Choose one of the two options:

Create and post two functions, f(x) and g(x), of the types we have considered so far in this course. Make the functions challenging, but not beyond what is covered in the textbook; avoid very simple examples.
Create and post a function, f(x), again, of a type we have already considered in this course.

To complete the discussion: To gain full credit for your work, you must

Choose one of the options above to make your initial post.
Then, you must choose a similar post from a classmate that no one else has chosen yet, and compute what is required:
- If the post from a classmate you chose to answer is from option 1) then you must find the compositions f(g(x)) and g(f(x)) of the two given functions.
- If the post from a classmate you chose to answer is from option 2) then you must compute the inverse of the given function f(x), and also verify that f(f -1(x)) = x