definition of a function

In the previous post we have discussed about How to Find the Domain of a Function and In today's session we are going to discuss about definition of a function. In this blog we will discuss the definition of a function. Function is used to show relationship among set of inputs and set of outputs in which every value of input is related to exactly one value of output. In other words a relation defined from I to J such that a sub set of I * J is called as function from I to J. Let's us understand the concept of function and its types. There are different types of function which are given as:

One – one function

Many one function

Onto function

Now we will have small introduction about all its types.

One – one function (it is also called as injection function): - A function f: I → J is said to be one – one function if every input value of element 'I' has different image in 'J'. So it can be written as:

f : I → J is one – one if value of 'i' not equal to 'j'. (i ≠ j) → f (i) ≠ f (j) for all ij Ԑ I.

Many one function: - A function f :I → J is said to be many one function if two or more elements of set 'I' have same images in 'J'. In mathematical form it can be written as:

f: I → J is a many one function if there exist a, b Ԑ I such that a ≠ b but f (a) = f (b).

Onto function: - A function f: I → J is said to be onto function or it is also said to be 'surjection' if every value of element 'J' is image of some element of 'I' that is if f (I) = J, and range of 'f' is co – domain of function 'f' or in other words elements of 'J' has no pre – image in element 'I'. This is all about types of functions.

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