Would there be no input or input does not exist?

Question

This problem is from Discrete Mathematics and Its Applications.

And the definition of inverse from the book:

For part 43 (c), would the inverse not exist? For the floor function, in terms of $f(a) = b$, there is no $a$ that will get you a value between $0$(exclusive) and 1(exclusive) because, by definition, the floor function returns an integer? Therefore the inverse ($0 < x < 1$) will not exist.

Answer 1

You are very close.

The correct answer is not really "does not exist" but ___.