
Integrating gives

To compute the integral, substitute
, so that
. Then

Since
for all
, we can drop the absolute value, so we end up with

Given that
, we have

so that

There are

such strings, provided that the ordering of the bits doesn't matter.
Answer: option A. The inverse of G(x) is not a function.
Because that means that for some values of x, say x = a and x = b, G(a) = G(b) = Z, then you cannot tell whether the value that generates Z corresponds to a or b.