\(\renewcommand{\d}{\displaystyle}\newcommand{\N}{\mathbb N}\newcommand{\inv}{^{-1}}\newcommand{\st}{:}\)
Let be the set of all numbers with three or fewer digits. Define the function by where and are the digits of the number in (write numbers less than 100 with leading 0’s to make them three digits). For example,
  1. Let Find
  2. Find
  3. Find
  4. Find
  5. Is injective? Explain.
  6. Is surjective? Explain.