
Let $X = \{n \in \N \st 0 \le n \le 999\}$ be the set of all numbers with three or fewer digits. Define the function $f:X \to \N$ by $f(abc) = a+b+c\text{,}$ where $a\text{,}$ $b\text{,}$ and $c$ are the digits of the number in $X$ (write numbers less than 100 with leading 0’s to make them three digits). For example, $f(253) = 2 + 5 + 3 = 10\text{.}$
1. Let $A = \{n \in X \st 113 \le x \le 122\}\text{.}$ Find $f(A)\text{.}$
2. Find $f\inv(\{1,2\})$
3. Find $f\inv(3)\text{.}$
4. Find $f\inv(28)\text{.}$
5. Is $f$ injective? Explain.
6. Is $f$ surjective? Explain.