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

Let [math]X = \{n \in \N \st 0 \le n \le 999\} be the set of all numbers with three or fewer digits. Define the function [math]f:X \to \N by [math]f(abc) = a+b+c\text{,} where [math]a\text{,} [math]b\text{,} and [math]c are the digits of the number in [math]X (write numbers less than 100 with leading 0’s to make them three digits). For example, [math]f(253) = 2 + 5 + 3 = 10\text{.}

- Let [math]
A = \{n \in X \st 113 \le x \le 122\}\text{.} Find [math]f(A)\text{.} - Find [math]
f\inv(\{1,2\}) - Find [math]
f\inv(3)\text{.} - Find [math]
f\inv(28)\text{.} - Is [math]
f injective? Explain. - Is [math]
f surjective? Explain.