How to implement f (g x) (h x) point-freely in Haskell?

Question

From this answer one learns how to implement the function \x y z -> f x (g y z) in a pointless way in Haskell, where f and g are functions. And my question is

How to write the function \x -> f (g x) (h x) in a pointfree manner in Haskell? Here f g h are functions for which f (g x) (h x) is defined.

The idea I currently have in mind is something like the following.

uncurry f (mapTuple ($ x) (g, h))

But several tries shows that this is fallacious; even the part map ($ x) [g, h] is suspicious: what if g and h have different ranges?

In addition, readability is not too much an issue here.

Any help is sincerely appreciated.

Answer 1

As melpomene suggested, \x -> f (g x) (h x) is equivalent to liftM2 f g h.

When you have question concerning how to convert Haskell code into pointfree Haskell code, you can just try Pointfree.io.

It is a great tool which often can tell you when NOT to use pointfree code because it goes completely unreadable sometimes :-)