Question

Let S = {a, b, c] and T = {1, 2, 3}. Find F-1 of the following functions F from S to T1, if it exists:

(i) F = {(a, 3), (b, 2), (c, 1)}

(ii) F = {(a, 2), (b, 1), (c, 1)}

Answer 1

S = {a, b, c} and T = {1, 2, 3}
(i) F = [(a, 3), (b, 2), (c, 1)}
i.e., F(a) = 3, F(b) = 2, F(c) = 1
⇒ F-1(3) = a, F-1(2) = b, F-1(1) = c
F-1 = {(3, a), (2, b), (1, c)}

(ii) F = {(a, 2), (b, 1), (c, 1)}
F is not one-one since elements b and c have the same image I.
∴ It is not a one-one function. So, its inverse does not exist.