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Two Restrictions That Define Special Function Types

publish date: 2026/05/23 18:47:51.803842 UTC

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The general definition of a function places two conditions only on elements of the domain. If we impose analogous restrictions on elements of the codomain, which two special function types result?

Constant function and polynomial function

One-one (injective) function and onto (surjective) function

Finite function and infinite function

Continuous function and discontinuous function

Correct Answer

One-one (injective) function and onto (surjective) function

Explanation

General functions only restrict domain elements: (i) every domain element has an image, (ii) each domain element has exactly one image. Restricting the codomain analogously gives: (i) every codomain element is an image → onto/surjective; (ii) each codomain element has at most one pre-image → one-one/injective.

Reference

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

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