Given the parametric function $f:\mathbb{R}^2 \rightarrow \mathbb{R}^2$ with $f(x,y) = (3x+2y,4x+3y)$. Is $f$ bijective?
So if you look at any given point $(\dot{x},\dot{y}) \in \mathbb{R}^2$ the system of linear equations should always be solvable:
(1): $\ 3x+2y = \dot{x}$
(2): $\ 4x+3y = \dot{y}$
Do i get $f$ is surjective from that? What about $f$ injective?