Question

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)}​

Answer 1

$\huge\star\mathfrak\red{{Answer:-}}$

Solution

(a) It is easy to see that f is one-one and onto, so that f is invertible with the inverse

f–1 of f given by f

–1 = {(1, 1), (2, 2), (3, 3)} = f.

(b) Since f (2) = f (3) = 1, f is not one-one, so that f is not invertible.

(c) It is easy to see that f is one-one and onto, so that f is invertible with

f–1 = {(3, 1), (2, 3), (1, 2)}.