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 10b
Whether the given function is one-to-one correspondence and also find the inverse of the given function if it exists.
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.
Let us check if the function is one-to-one or not.
If and are any two elements of such that,
Now, by the definition of the function ,
Divide both sides by to get the following:
Thus, the function is a one-to-one function.
Check if the function is onto or not.
Suppose is any even integer such that,
Thus, every element from the range has a pre-image
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