Algebra Solutions: Determine whether given relations are well-defined

Determine whether the following functions are well defined.

$f : \mathbb{Q} \rightarrow \mathbb{Z}$ given by $f(a/b) = a$ . This relation is not well defined since, in particular, $1/2 = 2/4$ but $f(1/2) = 1 \neq 2 = f(2/4)$ .
$f : \mathbb{Q} \rightarrow \mathbb{Q}$ given by $f(a/b) = a^2/b^2$ . This relation is well defined. Note that if $a/b = c/d$ , then $a^2/b^2 = c^2/d^2$ , and hence $f(a/b) = f(c/d)$ .

Algebra Solutions