\(\newcommand{\amp}{&}\)
We already know that [math] undoes the action of [math]
[math]
In this problem we will see what happens when we compose a function and its inverse in reverse order:
[math]
Consider the function [math] and its inverse:
[math]
and use them to answer the following.
  1. Evaluate the expression by working from the inside out. In the first blank, you are evaluating [math] where it is being entered inside parentheses as the input for [math] In the second blank, you are evaluating to get the final answer.
    [math] [math]
  2. Evaluate the expression by working from the inside out. In the first blank, you are evaluating [math] where it is being entered inside parentheses as the input for [math] In the second blank, you are evaluating to get the final answer.
    [math] [math]
You should notice that the function [math] undid the action of [math] In function notation, this says:
[math]

Solution: