sets – Is this way to combine two functions into a new function called a function product?

I have been looking for a maths operation that allows me to combine functions in a specific way. For example if we have functions f and g both with single mappings from o to e and v to c respectively, and we want to achieve whats below.

f ? g = {o -> e} ? {v -> c} = {(o,v) -> (e,c)}

I have been told that what I’m looking for is called a function product. I can’t find anything about this, also does it have a another name?

I’ve been told this is how to compute it, where X is called the function product.

(f X g)(x,u) = (f(x), g(u))

Which works, but I cant find anything about it online.