Select the correct answer. This table defines a function. Which table represents the inverse of the function defined above?
A.
B.
C.
D.
Answer (2)
To find the inverse of a function, swap the x and y values.
The original table has pairs ( 7 , 21 ) , ( 10 , 30 ) , ( 13 , 39 ) , and ( 16 , 48 ) .
Swapping the values gives pairs ( 21 , 7 ) , ( 30 , 10 ) , ( 39 , 13 ) , and ( 48 , 16 ) .
The table representing the inverse function is C: C .
Explanation
Understanding Inverse Functions To find the inverse of a function defined by a table, we simply swap the roles of x and y . This means that each ( x , y ) pair in the original table becomes a ( y , x ) pair in the inverse table.
Identifying Original Pairs The original table gives us the following pairs: ( 7 , 21 ) , ( 10 , 30 ) , ( 13 , 39 ) , and ( 16 , 48 ) .
Swapping x and y Swapping x and y in each pair, we get the following pairs for the inverse function: ( 21 , 7 ) , ( 30 , 10 ) , ( 39 , 13 ) , and ( 48 , 16 ) .
Finding the Correct Table Now, we need to find the table that represents these pairs. Looking at the options, we see that option C has x values of 21, 30, 39, and 48, and corresponding y values of 7, 10, 13, and 16. This matches the pairs we found for the inverse function.
Conclusion Therefore, the correct answer is C.
Examples
Understanding inverse functions is crucial in many real-world applications. For example, if you have a function that converts Celsius to Fahrenheit, the inverse function converts Fahrenheit back to Celsius. Similarly, in cryptography, inverse functions are used to decrypt encoded messages. In economics, if a function represents the supply of a product at a certain price, the inverse function represents the price at a certain supply. These examples highlight how inverse functions allow us to reverse a process or relationship, providing valuable insights and tools in various fields.
To determine the inverse of a function represented in a table, we simply swap the x and y values of each pair. The original pairs translate into inverse pairs which match option C, confirming that C represents the inverse function. Thus, the correct answer is C.
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