f:Z→Z   is given by f(x) = x3 is-

injective but not surjective injective and surjective both neither injective nor surjective surjective only

injective but not surjective

f:Z→Z   is given by f(x) = x3   It is seen that for x, y ∈ Z , f(x) = f(y)  ⇒ x3 = y3 ⇒ x =y So f is injective. Now, 2 ∈ Z, But there does not exist any element x in Z such that f(x) = x3 = 2 so f is not surjective. Hence, function f is injective but not surjective.