Math Problem Statement

Which of the following represents a one-to-one function?

Solution

The question asks which option represents a "one-to-one function." A one-to-one function (injective function) is a function where each element of the domain maps to a unique element in the codomain. No two different inputs can map to the same output.

Let's analyze the choices:

  1. A cellphone brand to its owner: This is not one-to-one because multiple owners can have the same cellphone brand.

  2. The president to its constituents: This is not one-to-one because a single president represents many constituents.

  3. A student to its LRN (Learner Reference Number): This is likely a one-to-one function, as each student is assigned a unique LRN, and no two students share the same LRN.

  4. A father to its child: This may not be one-to-one because a father can have multiple children, meaning one father could be mapped to multiple outputs.

The correct answer is "A student to its LRN", as this represents a one-to-one relationship where each student has a unique identifier (LRN).

Would you like more details or have any other questions?

Here are 5 related questions:

  1. What makes a function injective?
  2. Can a one-to-one function be a many-to-one function at the same time?
  3. How does a one-to-one function differ from a surjective function?
  4. What is the inverse of a one-to-one function?
  5. How can we test if a function is one-to-one?

Tip: To verify if a function is one-to-one, check if each input corresponds to a unique output and no two inputs share the same output.

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Math Problem Analysis

Mathematical Concepts

Functions
One-to-One Function

Formulas

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Theorems

Injective (One-to-One) Function Definition

Suitable Grade Level

Grades 9-12