
The following functions all have domain $\{1,2,3,4\}$ and codomain $\{1,2,3,4,5\}\text{.}$ For each, determine whether it is (only) injective, (only) surjective, bijective, or neither injective nor surjective.
1. $f = \twoline{1 \amp 2 \amp 3 \amp 4}{1 \amp 2 \amp 5 \amp 4}\text{.}$
2. $f = \twoline{1 \amp 2 \amp 3 \amp 4}{1 \amp 2 \amp 3 \amp 2}\text{.}$
3. $f(x)$ gives the number of letters in the English word for the number $x\text{.}$ For example, $f(1) = 3$ since “one” contains three letters.