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InterviewSolution
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Define the surjective function. Give an example. |
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Answer» Surjective Function A function f: A → B is said to be onto if every element in B has at least one pre-image in A. Thus, if f is onto then for each y ∈ B ∃ at least one element x ∈ A such that y = f(x) Also, f is onto range f = B Example: Let N be the set of all natural numbers and let E be the set of all even natural numbers Let f: N → E: f(x) = 2x Ɐ x ∈ N Then, y = 2x => x = ½ y Thus, for each y ∈ E there exists ½ y ∈ N such that f(1/2 y) = (2 × ½ y) = y Hence, f is onto. |
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