An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
A one-to-one function requires each f ( x ) value to correspond to a unique x value.
The first table has f ( 14 ) = f ( 12 ) = 197 , so it is not one-to-one.
The second table has f ( − 2 ) = f ( 2 ) = 5 and f ( − 1 ) = f ( 1 ) = 2 , so it is not one-to-one.
Therefore, neither relation represents a one-to-one function. Neither
Explanation
Understanding One-to-One Functions A one-to-one function is a function where each element of the range is associated with at most one element of the domain. In simpler terms, for every y value, there is only one x value that corresponds to it.
Analyzing the First Table In the first table, the f ( x ) value of 197 appears twice, for x = 14 and x = 12 . This means that there are two different x values that map to the same f ( x ) value. Therefore, the first table does not represent a one-to-one function.
Analyzing the Second Table In the second table, the f ( x ) value of 5 appears twice, for x = − 2 and x = 2 . Also, the f ( x ) value of 2 appears twice, for x = − 1 and x = 1 . This means that there are two different x values that map to the same f ( x ) values. Therefore, the second table does not represent a one-to-one function.
Conclusion Since neither table represents a one-to-one function, the answer is that neither relation represents a one-to-one function.
Examples
One-to-one functions are useful in cryptography, where each input needs to produce a unique output to ensure secure encryption. They are also used in data analysis to ensure that each data point is uniquely identified.
