What is the terminology for a "reversible" binary function, such that of we can compute the result from two operands, that is $f(x,y) = z$, then we can also compute one operand from the result and the other operand, that is $g(x,z) = y$?
For example, with addition if we know $x + y = z$ we can compute $x = z - y$, but we can't do the same for $\min(x,y)=z$. The context of this in terms of Fenwick trees and range queries: we can compute prefix sums for $\min$, but not arbitrary range queries like sums where $\sum a[l,r] = p[r] - p[l-1]$, ($p$ is the prefix sums).
In terms of algebra, I think this is maybe not a property of the binary function but the existence of inverses. For an associative operation, $x * y = z$ lets us compute $x * y * y^{-1} = z * y^{-1}$ if $y^{-1}$ exists.