Question

Asked Jan 26, 2020

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Let S = {1, 2, 3}. Determine whether the functions f : S → S defined as

below have inverses. Find f^{-1}, if it exists.

(a) f = {(1, 1), (2, 2), (3, 3)}

(b) f = {(1, 2), (2, 1), (3, 1)}

(c) f = {(1, 3), (3, 2), (2, 1)}

Step 1

A function has an inverse iff f is one-one onto.

If inverse of f exists then we have

Step 2

(a) Here f is one-one onto , so inverse of f exist

Step 3

(b) Here f is not one-one as f(2)=f(3)=1 .Also f is not onto because there ...

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