mekso ternary operator: inverse function of input function X_{1} with respect to its input X_{2}, taken on branch or restricted domain X_{3} ("domain" being of X_{1}).

The output of this function is itself a function of the same arity as X_{1}. X_{3} often omitted due to obviousness (or due to lack of need/due to well-definition) or convention. X_{1} should be a function supplied in "zau'au" quotes; that function itself should be at least unary and the input against which the inverse is being taken in an n-ary X_{1} is X_{2}. X_{2} should technically be a input slot index or domain (or subspace/projection thereof), but a named and non-evaluated dummy variable symbol can be supplied if the slot ordering or domain terms (vel sim.) are not well-specified. Because the output is a function, it can itself (that is: the output's self) have an input; use "bai'i'i" or an equivalent thereof for this purpose in most situations. For example, if f(x,y,z)=w,g=fau'i(f,2),v=(x,y,z), and u=bai'i'i(v,2,w)=(x,w,z), then g(u)=f^-1_{2(x,w,z)}=y. In English notation, "fau'i(f,n)" might be notated as "inv(f,n)". See also: "fau'e" (this word acts as a better-specified case of iteration order n=-1 for "fau'e").