Find a formula knowing input and output

what? xD

i remember something from mathematical analysis, where you use matrices and transformation to do something like that...but not sure if you can do that with those imputs/outputs...
you need math skills lvl 43 to solve that thing.

You'd need the code key in order to solve such combinations. Of course, it all depends on whether or not you are actually dealing with an encryption of sorts or if it's just a combination of letters which, when solved, output another combination needed for something else...basically, you have to ask yourself: Is it supposed to become a plain text combination or "just" a combination?

Encryption methods like Caesar shift the letters of a word/sentence by X to the right, with X being the "code key". So, the word "Steamgifts" will become "Tufbnhjgut" with Caesar. Now look...

Steamgifts

Tufbnhjgut

Upon closer inspection, you should notice that "S" became a "T", that "t" became an "u", etc. This means the code key here is 1. Using 2 as the code key transforms the word "Steamgifts" to "Uvgcoikhvu".

Long story short: You need the code key, or else all you can do is guess.

possible in linear algebra with estimation. But it's only for linear graphs.
You can have points or lines or vectors or even a combination of them as inputs, then you can find the formula for them.

What you're asking is more like crypto

Thank you all for the answer :)
It seems to be much more complicated than what I expected :P