Question

X and Y are two sets and f: X → Y. If {f(c) = y; c ⊂ X, y ⊂ Y} and {f ⁻¹(d) = x; d ⊂ Y, x ⊂ X}, then the true statement is

(A)  f[f ⁻¹(b)] = b

(B)  f ⁻¹[f(a)] = a 

(C)  f[f ⁻¹(b)] = b, b ⊂ y

(D)  f ⁻¹[f(a)] = a, a ⊂ x

Answer 1

Correct option (D) f ⁻¹[f(a)] = a, a ⊂ x

Explanation :

The given data is shown in Fig. Since f^-1 (d) = x, we get Now, if  a ⊂ x, f(a) ⊂ d, we get f ^–1[f(a)] = a.