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One-One (Injective) Function — Definition
publish date: 2026/05/23 18:47:46.689737 UTC
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The diagram below shows a mapping from set A to set B.
Which property does this mapping illustrate?
Correct Answer
One-one (injective): distinct domain elements map to distinct images
Explanation
A function is one-one (injective) if distinct inputs always produce distinct outputs: for every \(a_1, a_2 \in A\), \(f(a_1) = f(a_2) \Rightarrow a_1 = a_2\). In the diagram, a, b, c map to 1, 2, 3 respectively — all different. Element 4 in B is not hit by anyone — that is allowed for an injective function; it only means the function is not onto.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012