One application that is useful and took me some time to figure out from the very short description at learn you a haskell: Since:
f $ x = f x
and parenthesizing the right hand side of an expression containing an infix operator converts it to a prefix function, one can write ($ 3) (4+)
analogous to (++", world") "hello"
.
Why would anyone do this? For lists of functions, for example. Both:
map (++", world") ["hello","goodbye"]`
and:
map ($ 3) [(4+),(3*)]
are shorter than map (\x -> x ++ ", world") ...
or map (\f -> f 3) ...
. Obviously, the latter variants would be more readable for most people.