Bijective function

Sure. Here's one:

f(0) = 1
f(1) = 0
f(n) = n, for n > 1

What about

f(n) = n - 1

That maps 0 to -1, but the domain and range are non-negative integers.

Actually, markr, the way you defined the function actually spoils the whole spirit of the question , because in your solution you directly use f ( 1) = 0 for defining the function , still it was a good approach.

I thought it was a question about existence. Perhaps you prefer this:

f(x) = x xor 1

I think I should modify the question I asked , one can of course have a bijective function defined on non-negative set of integers such that f ( 1 ) = 0 the fact that such a bijection exists is trivial ,
the question is to find an explicit formula for such a bijective function ;
and this one to markr , which xor operation are you using ? can you please be more specific .

bitwise exclusive or
Take the binary representation of the input and flip the least significant bit.

thanks