In J (a sort of dialect of APL), there's a thing called "under", written "&.". The expression "(f &. g) x" is equivalent to "(g^:_1) (f (g x))" where "g^:_1" is J's "obverse" of g, which in cases where it exists is usually the inverse of g (
http://www.jsoftware.com/help/dictionary/intro26.htm). Abusing notation with some weird mixture of Haskell and J, this means that "((+) &. log)" multiplies numbers by taking logs, adding and exponentiating. You "inv" is "under" for cases where g == g^-1 (reverse being a good example). In cases where g /= g^-1, it's obviously a useful operation, but the case where g == g^-1 seems a bit specialised. Can you think of any other useful cases than g == reverse? I guess "inv (1/) sum" is the harmonic mean, but that's another special case.