Q. 41

# 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.

Formula:-

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

such that gof =Ix and fog = Iy .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)}.

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