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 12a
Whether the given function is one-to-one correspondence and also find the inverse of the given function if it exists.
is defined by the rule , for all integers .
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.
The objective is to determine whether the following function is one-to-one correspondence or not
and to find the inverse function.
is defined as , for all integers .
To show that is a one-to-one correspondence, need to show that is one-to-one and is
Suppose such that .
Then by the definition of ,
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