Types of Function
Different Types of Functions are used to solve various types of mathematical problems especially related to curves and equations. There are three major types functions in mathematics that are based on the element mapping from set A to set B.
Injective function or One to One Function
The function in which each element of the domain has a distinct image in the codomain is called the Injective or One-to-One function.
f: A → B is said to be one-to-one or injective if the images of distinct elements of A under f are distinct, i.e.,
f(a1) = b1, f(a2) = b2
where a1, a2 ∈ A and b1, b2 ∈ B
Surjective functions or Onto Function
Surjective Function is the function in which every element of codomain has a pre-image in the domain. It is also called Onto Function which means each element of codomain is associated with each element of the domain. No element of codomain should have an empty relation. The number of elements of codomain and range is the same.
f: A → B is said to be onto, if every element of B is the image of some element of A under f, i.e., for every b ϵ B, there exists an element ‘a’ in A such that f(a) = b.
Bijective Function
If a function has properties of both Injective(One to One) and Surjective(Onto function) then the function is called a Bijective Function. In Bijective Function, each element of the domain is related to each element of the codomain and also there is one-to-one relation. This implies that number of elements of the codomain and range are the same and no element either in the domain or codomain has empty relation.
Based on the output values, the functions classified as odd and even functions. Let’s have a look on them
Odd Functions
Odd function is a type of function that exhibits symmetry about the origin. Specifically, if f(x) is an odd function, it exhibits that f(-x) = -f(x)
Even Function
Even function is a type of function that exhibits symmetry about the y-axis. Specifically, if f(x) is an even function, it exhibits that f(-x) = f(x)
What is a Function in Maths?
A Function in maths is a special relation between the set of input values and the set of output values. In Function, each input value gives a particular output value. We represent a function in maths as, y = f(x) where x is the input value and for each x we get an output value as y.
In this article, we will learn about, functions in mathematics, their various types, examples, and others in detail.
Table of Content
- What is a Function in Maths?
- Function Definition in Maths
- Functions Examples
- Condition for a Function
- Representation of Functions in Math
- Identification of Function
- Types of Function
- What is a Function in Algebra?
- Domain and Range of a Function
- Composition of Functions
- Algebra of Functions
- What is a Function on a Graph?
- Graphing Functions
- Common Functions
- Applications of Functions
- Examples on Function
- Practice Problems on What is a Function
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