Question 17 (5 points)
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Which of the following is the inverse relation of the set?
A) {(-2,5),(-3,3),(6,4),(-7,-1)}
B) {(-3,5),(-2,3),(-1,4),(-7,6)}
C) {(2,-5),(3,-3),(-6,-4),(7,1)}
D) {(-4,10),(-6,6),(12,8),(-14,-2)}
Question 18 (5 points)
Answer (1)
To find the inverse relation, the x and y coordinates of each ordered pair are swapped. The inverse of {(5,-2),(3,-3),(4,6),(-1,-7)} is found by swapping the coordinates: (5, -2) becomes (-2, 5), (3, -3) becomes (-3, 3), (4, 6) becomes (6, 4), and (-1, -7) becomes (-7, -1). The inverse relation is {(-2,5),(-3,3),(6,4),(-7,-1)}. The final answer is {( − 2 , 5 ) , ( − 3 , 3 ) , ( 6 , 4 ) , ( − 7 , − 1 )} .
Explanation
Understanding Inverse Relations To find the inverse of a relation, we simply swap the x and y coordinates of each ordered pair in the set.
Swapping Coordinates Given the set {( 5 , − 2 ) , ( 3 , − 3 ) , ( 4 , 6 ) , ( − 1 , − 7 )} , we swap the coordinates of each pair:
(5, -2) becomes (-2, 5)
(3, -3) becomes (-3, 3)
(4, 6) becomes (6, 4)
(-1, -7) becomes (-7, -1)
The Inverse Relation So, the inverse relation is {( − 2 , 5 ) , ( − 3 , 3 ) , ( 6 , 4 ) , ( − 7 , − 1 )} .
Identifying the Correct Option Comparing this with the given options, we see that option A matches our result.
Final Answer Therefore, the inverse relation of the set {( 5 , − 2 ) , ( 3 , − 3 ) , ( 4 , 6 ) , ( − 1 , − 7 )} is {( − 2 , 5 ) , ( − 3 , 3 ) , ( 6 , 4 ) , ( − 7 , − 1 )} .
Examples
Understanding inverse relations is crucial in many areas of mathematics and real-life applications. For example, consider a function that converts Celsius to Fahrenheit. The inverse function would convert Fahrenheit back to Celsius. In economics, if a function represents the demand for a product at a certain price, the inverse function would represent the price at which a certain quantity is demanded. This concept helps in reversing processes or understanding reverse dependencies, providing valuable insights in various fields.
