In 44-55 indicate which of the function in the referenced exercise are one-to-one correspondences. For each function that is a one-to-one correspondence, find the inverse function.

Exercise 22

To check:

Whether the given function is one-to-one correspondence and also find the inverse of the given function if it exists.

Given information:

Let S be the set of all strings of 0's and 1's and define D:S→ℤ as follows:

For all s∈S, D(s)= the number of 1's in s minus the number of 0's in s.

Concept used:

One-to-one function: The distinct elements in domain are mapped with distinct elements in co-domain.

Onto function: Every element in co-domain must be mapped with the element in domain