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

Question

A question I got on my last interview:

Design a function f, such that:

f(f(n)) == -n

Where n<

Answer 1

The question doesn't say anything about what the input type and return value of the function f have to be (at least not the way you've presented it)...

...just that when n is a 32-bit integer then f(f(n)) = -n

So, how about something like

Int64 f(Int64 n)
{
    return(n > Int32.MaxValue ? 
        -(n - 4L * Int32.MaxValue):
        n + 4L * Int32.MaxValue);
}

If n is a 32-bit integer then the statement f(f(n)) == -n will be true.

Obviously, this approach could be extended to work for an even wider range of numbers...