Determining if a function is injective

MHB
Thread starter markosheehan
Start date Jul 16, 2016
Tags

Function Injective

In summary, to determine if a function is injective, you can use the "horizontal line test". An injective function is one in which each element in the domain maps to a unique element in the range. Yes, a function can be both injective and surjective, which is called a bijective function. To prove that a function is injective, you can use the definition of an injective function or a more mathematical approach. There is no difference between a one-to-one function and an injective function, as they both refer to a function with unique mappings between the domain and range.

Jul 16, 2016

markosheehan

is the function x³-5x²+3x+5 injective. how can you tell

Physics news on Phys.org

Jul 16, 2016

Evgeny.Makarov

Gold Member

MHB

Re: calculus

You can determine if the function has a local extremum. If a function is continuous and has, say, a maximum, then it is not injective since it assumes the same values on both sides of that point of maximum.

Related to Determining if a function is injective

1. How do you determine if a function is injective?

To determine if a function is injective, you can use the "horizontal line test". This involves drawing a horizontal line anywhere on the graph of the function. If the line intersects the graph at more than one point, then the function is not injective. If the line only intersects the graph at one point, then the function is injective.

2. What is the definition of an injective function?

An injective function is one in which each element in the domain maps to a unique element in the range. In other words, no two elements in the domain can map to the same element in the range.

3. Can a function be both injective and surjective?

Yes, a function can be both injective and surjective. This type of function is called a bijective function. In a bijective function, every element in the domain maps to a unique element in the range, and every element in the range has a corresponding element in the domain.

4. How can you prove that a function is injective?

To prove that a function is injective, you can use the definition of an injective function. You can show that no two elements in the domain map to the same element in the range, or you can use a more mathematical approach such as a proof by contradiction.

5. What is the difference between a one-to-one function and an injective function?

There is no difference between a one-to-one function and an injective function. They both refer to the same concept of a function where each element in the domain maps to a unique element in the range. The terms are simply used interchangeably in different contexts.