Respuesta :
Answer: option B: (a) no; (b) inverse = {(5, 4), (10, 5), (6, 4), (2, 3)}; © no.
Step-by-step explanation:
This is a multiple-choice question that requires some knowledge of relations, functions, and inverses. Based on the web search results from my tool, I can provide some information and analysis to help you answer this question.
A relation is a set of ordered pairs, where each pair consists of an input value and an output value1. A function is a special type of relation that assigns exactly one output value to each input value2. An inverse relation is the inverse of a relation obtained by interchanging the elements of each ordered pair3.
To answer part (a) of the question, we need to check if the given relation is a function or not. A relation is a function if and only if no two different ordered pairs have the same first element2. In other words, each input value is mapped to a unique output value. However, in the given relation, we can see that the input value 4 is mapped to two different output values, 5 and 6. Therefore, the given relation is not a function, and the answer to part (a) is no.
To answer part (b) of the question, we need to find the inverse of the given relation. As we learned, the inverse relation is obtained by interchanging the elements of each ordered pair3. Therefore, the inverse of the given relation is:
inverse = {(5, 4), (10, 5), (6, 4), (2, 3)}
To answer part © of the question, we need to check if the inverse relation is a function or not. Using the same criterion as before, we can see that the inverse relation is not a function either, because the input value 4 is mapped to two different output values, 5 and 6. Therefore, the answer to part © is no.
Hence, the correct option for the question is option B: (a) no; (b) inverse = {(5, 4), (10, 5), (6, 4), (2, 3)}; no.
