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$\newcommand{\twoline}[2]{\begin{pmatrix}#1 \\ #2 \end{pmatrix}}\newcommand{\amp}{&}$

The following functions all have $\{1,2,3,4,5\}$ as both their domain and codomain. For each, determine whether it is (only) injective, (only) surjective, bijective, or neither injective nor surjective.

$f = \twoline{1 \amp 2 \amp 3 \amp 4 \amp 5}{3 \amp 3 \amp 3 \amp 3 \amp 3}\text{.}$

$f = \twoline{1 \amp 2 \amp 3 \amp 4 \amp 5}{2 \amp 3 \amp 1 \amp 5 \amp 4}\text{.}$

$f(x) = 6 - x\text{.}$

$f(x) = \begin{cases} x/2 \amp \text{ if } x \text{ is even} \\ (x+1)/2 \amp \text{ if } x \text{ is odd}\end{cases}\text{.}$