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Diagram — Is This Function Onto?

publish date: 2026/05/23 18:47:50.986927 UTC

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Examine the mapping below carefully.

Set A Set B f 1 2 3 1 2 3

Is this function onto (surjective)?

Correct Answer

No — element 3 in the codomain has no pre-image in A

Explanation

For surjectivity, every element of the codomain must be the image of at least one domain element. In this diagram, element \(3\) (shown greyed out) is never hit — neither \(a\), \(b\), nor \(c\) maps to it. Therefore the range is only \(\{1, 2\}\) which is a proper subset of the codomain \(\{1, 2, 3\}\), so the function is not onto.

Reference

Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012

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