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.

I'm not very good at this subject, so sorry if this is a stupid question. Any hints are appreciated, thanks.


Question: PhotoShop CC 2014 uses too much disk space
Answer: Maybe this should be written as comment. But my reputation is quite low to add a comment.

Anyway, I didn't use CC version yet. I've used Photoshop CS6 so far. Photoshop has a performance settings option that lets you choose the amount of RAM, Scratch Disk and Cache size for images.

You can go to the Edit > Preferences > Performance.
Now set your delegated RAM for Photoshop, History and Cache Size. 
Also choose your scratch disk. 

And you should also check the amount of virtual RAM available. You can increase your virtual RAM as - 

Right Click on My Computer > Properties > Advanced > Performance > Settings > Advanced > Virtual Memory > Change > Uncheck Automatic Option > Custom > Choose a Volume for Virtual RAM > Set Custom Virtual RAM.

Note: If your RAM is 8 GB, you can set another 8 GB as virtual RAM. Or more if you want. 

Waiting for your response. Inform us whether this system works or not. Thanks.