In Maths, a function is defined as a relation in which the set of outputs are derived from the set of inputs. Here, each input is exactly related to the one output. Let us take if the object “x” is in the set of inputs (domain), y is in the set of output (codomain), then the function “f” from x to y is defined by:
f: x → y
There are different types of functions in Maths that represent many equations in the Graph. Some of the functions are identity functions, linear functions, quadratic functions, exponential functions, polynomial functions, rational functions, modulus functions, and so on. But mostly the term “function” describes the below types of functions that represent the relations between the set of inputs and outputs. The important types of functions are:
- One to One Function
- Many to One Function
- Onto Function
- One to one and Onto Function
Let us discuss the types of function here in detail.
One to One Function
A function is said to be a one to one function if, for each element of A, there exists a distinct element of B. It is also known as an injective function. Let us take if x ∈ A, and y ∈ B, then the function is defined as f: A → B such that f(x) = f(y)
Many to One Function
Many to one function is a function, in which two or more elements of A have the same image in B. It means that two or more elements in the domain are mapped to the same element in the codomain.
Onto Function
The onto function is also known as a surjective function. There exists a function, where every element of the codomain, there are preimages in the domain known as onto function.
One to One & Onto Function
One-one and onto function is also known as one to one correspondence or bijective function. The function is said to be a bijective function if it satisfies the property of both injective and surjective function.
Thus, in Mathematics “functions” play a major role and it is applied in various concepts such as sequences and series for finding the missing numbers, solving linear, quadratic, polynomial, exponential equations, and so on.
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