Math Problem Statement
Solution
The problem concerns the definition of an onto function (also known as a surjective function). Let's analyze the statements:
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Every element in the co-domain must have an arrow pointing to it from some element of the domain.
This is correct. An onto function ensures that every element of the co-domain is mapped to by at least one element of the domain. This is a defining property of surjective functions. -
Every element in the domain must have an arrow pointing to it from some element of the co-domain.
This statement is incorrect. This would describe an injective or one-to-one relationship in the reverse sense, which is not relevant for surjectivity.
Thus, the correct answer is A. I only.
Would you like further clarification? Here are some related questions for practice:
- What is the definition of an injective function?
- How does a bijective function differ from an onto function?
- Can a function be both injective and surjective? If so, what is it called?
- What are some real-life examples of surjective functions?
- How can you verify if a function is surjective given its formula?
Tip: To check if a function is onto, ensure that every value in the co-domain is reachable by some input in the domain.
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Math Problem Analysis
Mathematical Concepts
Functions
Onto Functions
Surjective Functions
Formulas
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Theorems
Definition of Surjective (Onto) Functions
Suitable Grade Level
Grades 9-12
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