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 11b
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 real numbers
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.
Define by the rule , for all real numbers
The objective is to determine one-to-one correspondence of the given function, if it is a one-to-one correspondence, find the inverse function.
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 ,
Add on both sides to get the following:
Divide both the sides by to get the following:
Thus, the function is one-to-one function.
Let us check if the function is onto or not.
Suppose is any real number, such that
Thus, every element from the range has a pre-image
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started