Definition of a Surjective Function and a Function that is NOT Surjective

TL;DR

Subjective functions, also known as onto mappings, are functions in which every element in the codomain has a corresponding element in the domain.

Transcript

hello in this video we're briefly going to discuss subjective functions and do a very simple example so let's start with the definition a mapping which let's call F and let's use A and B from A to B so a here is called the domain and B is called the codomain is subjective another word for subjective is onto if for all Y and B so for every element i... Read More

Key Insights

• ❓ Subjective functions, or onto mappings, ensure that every element in the codomain has a corresponding element in the domain.
• 👈 Graphically, subjective functions can be represented by showing that every point on the y-axis has a corresponding point on the x-axis.
• ❎ The function f(x) = x^2 is an example of a function that is not subjective since it does not have corresponding values for negative numbers.
• ❓ Violating the definition of a subjective function requires producing just one element in the codomain that does not have a corresponding element in the domain.
• 👻 Subjective functions can allow for multiple elements in the domain mapping to the same element in the codomain.
• 🧡 The range of subjective functions can vary depending on the function's definition and domain.
• 😫 Subjective functions are important in mathematics for understanding mappings between sets.

Questions & Answers

Q: What is a subjective function?

A subjective function, also known as an onto mapping, is a function where every element in the codomain has at least one corresponding element in the domain.

Q: How can subjective functions be represented graphically?

Subjective functions can be represented graphically by showing that for every point on the y-axis, there is a corresponding point on the x-axis that maps to it.

Q: Why is the function f(x) = x^2 not subjective?

The function f(x) = x^2 is not subjective because it does not have corresponding values for negative numbers in the codomain. The range of the function is from 0 to infinity.

Q: Can subjective functions have multiple elements in the domain mapping to the same element in the codomain?

Yes, subjective functions can have multiple elements in the domain mapping to the same element in the codomain. The important requirement is that every element in the codomain has at least one corresponding element in the domain.

Summary & Key Takeaways

• Subjective functions, or onto mappings, are defined as functions where for every element in the codomain, there exists an element in the domain that maps to it.

• Graphically, this means that for every point on the y-axis, there is a corresponding point on the x-axis that maps to it.

• An example is given using the function f(x) = x^2, which is not subjective since it does not have corresponding values for negative numbers.