binary function game

[vh]

how to play:
someone posts a few useful cases of a binary function being applied. everyone else guesses what the function is. whoever guesses correctly gets to go next. if no one wins, anyone can post after 3 days.

example:

A:
let
foo(1, 1) = 2
foo(2, 2) = 5
foo(2, 3) = 5
foo(17, 13) = 30

B:
is it addition?

A:
no. 2+2 is not 5

C:
is it addition with the sole adjustment that 2+2 = 5?

A:
yes

endexample

question: but then can't anyone define some crazy function which works like multiplication, but 12839 * 28349 is actually defined to be -2389?

answer: yes, but that's a stupid function and don't do it because it'll make you look stupid. 2+2 =5 is only ok because it's a cultural meme and also something something 1984.

question: do the inputs have to be natural numbers?

answer: no, they can be anything. using mathematical objects are encouraged

starting function:

Q(sqrt, 16) = 2
Q(double, 3) = 12
Q(id, 1) = 1

go!