Let bitstrings have a maximum length of L bits.
and f(x)=number of one-bits less number of zero-bits.
x=length of bitstring in bits.
Case 1: x=L, all L bits are ones
Then f(x)=L
Case 2: x=L, all L bits are zeroes
Then f(x)=-L
Then
dom f(x)=[0,L]
range f(x) = [-L,L]
