HOW TO IDENTIFY THE TYPE OF FUNCTION IN SET THEORY

One to One Function

A function f : A -> B is called one – one function if distinct elements of A have distinct images in B.

A one-one function is also called an injection.

Many to One Function

A function f : A -> B is called many-one function if two or more elements of A have same image in B.

In other words, a function f : A-> B is called many-one if f it is not one–one.

Onto Function

A function f : A -> B is said to be onto function if the range of f is equal to the co-domain of f.

In other words, every element in the co-domain B has a pre-image in the domain A. An onto function is also called a surjection.

One to One and Onto Function

A function f : A -> B is called an into function if there exists atleast one element in B which is not the image of any element of A.

In other words, every element in the co-domain B has a pre-image in the domain A. An onto function is also called a surjection.

Into Function

Distinct elements of A have distinct images in B and every element in B has a pre-image in A.

Constant Function

A function f : A -> B is called a constant function if the range of f contains only one element. That is, f (x ) = c , for all x ∊ A and for some fixed c ∊ B .

Identity Function

Let A be a non–empty set. Then the function f : A -> A defined by f (x) = x for all x ∊ A is called an identity function on A and is denoted by I_A.

Real Valued Function

A function f : A -> B is called a real valued function if the range of f is a subset of the set of all real numbers ℝ . That is,f (A) ⊆ ℝ

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