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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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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

-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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