Designing function f(f(n)) == -n

Question

You didn’t say what kind of language they expected… Here’s a static solution (Haskell). It’s basically messing with the 2 most significant bits:

f :: Int -> Int
f x | (testBit x 30 /= testBit x 31) = negate $ complementBit x 30
    | otherwise = complementBit x 30

It’s much easier in a dynamic language (Python). Just check if the argument is a number X and return a lambda that returns -X:

def f(x):
   if isinstance(x,int):
      return (lambda: -x)
   else:
      return x()