Determine whether f is a function from the set of all bit strings to the set of

Question:

Determine whether f is a function from the set of all bit strings to the set of integers if
a) f (S) is the position of a 0 bit in S.
b) f (S) is the number of 1 bits in S.
c) f (S) is the smallest integer i such that the ith bit of S is 1 and f (S) = 0 when S is the empty string, the string with no bits.