\(\renewcommand{\d}{\displaystyle}\newcommand{\N}{\mathbb N}\newcommand{\inv}{^{-1}}\newcommand{\st}{:}\)

Let [math] be the set of all numbers with three or fewer digits. Define the function [math] by [math] where [math] [math] and [math] are the digits of the number in [math] (write numbers less than 100 with leading 0’s to make them three digits). For example, [math]
  1. Let [math] Find [math]
  2. Find [math]
  3. Find [math]
  4. Find [math]
  5. Is [math] injective? Explain.
  6. Is [math] surjective? Explain.