Let A = {a, b, c, d} and f : A → A be given by f = {(a, b), (b, d), (c, a), (d, c)}, write f –1 .

Question

Philoid · Accepted Answer

Formula:-

(i)A function f : X → Y is defined to be invertible, if there exists a function g : Y → X

such that gof =I_x and fog = I_y .The function g is called the inverse of f and is denoted by f^-1

(ii)A function is onto function or surjection if

Range (f)=co-domain(f)

Given:-

(i)A = {a, b, c, d}

(ii)f : A → A

(iii)f = {(a, b), (b, d), (c, a), (d, c)}

f is one-one since each element of A is assigned to distinct element of the set A. Also, f is onto since f (A) = A.

f^-1= {(b, a), (d, b), (a, c), (c, d)}.