Please answer all parts to this question

Please explain your answers/show work

(2) Define a function f from the set N+ to the set of binary strings as follows: Write a number n in standard binary notation (with no redundant leading Os). Then define f(n) to be the string you get by removing the leading '1'. For example, 5 in binary is 101, so f(5) = 01. (a) Is this function one-to-one? (b) Is it onto the set {0, 1}* of all binary strings? What happens with the empty string? (c) Now suppose we want to extend the domain of f to include zero. Let's call that a new function f':N + {0, 1}* where f'(0) "O" (that is, the binary string of just one 0 char) and f'(n) = f(n) for numbers n > Re-answer questions (a) (b) for f' in place of f. (d) How about if we try defining f'(0) = e instead