I know how to prove if a single variable function is injective or surjective but I've been quite confused by an exercise where i need to determine if:
$f :\mathbb{Q}^{2} \to\mathbb{Q}^{2}$
$f(x,y) = (x+y, x-y)$
is injective and/or subjective.
Is it possible to say that this function is not injective because:
$Let \;x_{1} = \frac{1}{2} and \;y_{1} = \frac{0}{2}, f(x_{1},y_{1}) = \frac{1}{2}$
$Let \;x_{2} = \frac{1}{2} and \;y_{2} = \frac{0}{4}, f(x_{2},y_{2}) = \frac{1}{2}$
$f(x_{1},y_{2}) = f(x_{2},y_{2}) \land (x_{1}, y{1}) \neq(x_{2}, y{2})$
Also, I assume this function would be surjective but how to prove with couples?
Anyone could point me in the right direction? Thanks!