Consider the function $\theta:\{0,1\}\times\mathbb{N}\rightarrow\mathbb{Z}$ defined as $\theta(a,b) = a-2ab+b$. Is this function bijective?
For injective, I tried doing the contrapositive by supposing $\theta(a,b)=\theta(c,d)$, then $a-2ab+b=c-2cd+d$, but I have no idea where to go from there. I tried solving for a and b separately and plugging it back in, but that just turned into a huge algebraic mess.
I haven't figured what I'm going to do for surjective yet.