A correspondence that works for all n

Let fn be the function that takes an

n-bit bitstring and flips only the first bit.

For example,

0010011 ? 1010011

1001101 ? 0001101

110011 ? 010011

101010 ? 001010

1. fn : On ?En?

2. fn is one-to-one? i.e. x ? y ? fn (x) ? fn (y)

3. fn is onto? i.e. for all y ? En,

there exists an x ? On such that fn (x)=y