volume_mute
Range and Codomain in an Onto Function
publish date: 2026/05/23 18:47:48.490711 UTC
volume_mute
For an onto (surjective) function \(f: A \to B\), which of the following is always true?
Correct Answer
The range of f equals the codomain B
Explanation
By definition, \(f: A \to B\) is onto if every element of \(B\) is the image of some element of \(A\). This means the range \(f(A)\) equals the entire codomain \(B\): \(f(A) = B\). For a function that is not onto, \(f(A) \subsetneq B\) — at least one codomain element has no pre-image.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012