InterviewSolution
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Let A = {2, 3, 4, 5} and B = {7, 9, 11, 13}, and let f = {(2, 7), (3, 9), (4, 11), (5, 13)}. Show that f is invertible and find f -1. |
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Answer» We know that f (2) = 7, f (3) = 9, f(4) = 11 and f (5) = 13 Here dom (f) = {2, 3, 4, 5} = A and range (f) = {7, 9, 11, 13} = B So different element in A have different image. f is one-one. range (f) = B where f is onto Hence, f is one-one onto and invertible. We know that f (2) = 7, f (3) = 9, f(4) = 11 and f (5) = 13 So we get f -1 (7) = 2, f -1 (9) = 3, f -1 (11) = 4, f -1 (13) = 5 Therefore, f -1 {(7, 2), (9, 3), (11, 4), (13, 5)}. |
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