# Functions In Discrete Mathematics

A function in discrete Math named ‘g’ from the Set ‘P’ to ‘Q’ is a relation from P to Q that satisfies the below conditions-
For each value of ‘a’ belonging to ‘P’, there will exist a unique value ‘b’ which belongs to ‘Q’ with both the values of ‘a’ and ‘b’ belonging to the function ‘g’. The set ‘P’ is the Domain of the function ‘g’ and ‘Q’ is the co domain or range of the function ‘g’. A function ‘g’ from P to Q is denoted as g: P → Q.

Suppose that ‘P’ and ‘Q’ are two non empty Sets then the function g: P → Q is a one to one or can be named as injective function if no two elements of ‘P’ are mapped to the same element of ‘Q’ that is for ‘a’ and ‘b’ belongs to ‘P’ and the Functions g (a) and g (b) belongs to ‘Q’, with the condition that a is not equal to ‘b’ that implies the result that g (a) also not equal to g (b).

A Onto function is there for every ‘b’ which belongs to ‘Q’ satisfy the condition g (a) = g (b).  A function will be bijective if it is both one- one and onto. The real values in discrete mathematics which are assigned to each number ‘x’ belongs to ‘R’ for a particular value y = g (x) where ‘y’ also belongs to ‘R’.

Some points are there which should be remembered to understand the Functions in discrete mathematics. A proposition can be said as a function from situations to the truth values T, F. A propositional operator can be said as a function taken from the ordered pairs of truth values to the truth values.

## One-to-One

A function (denoted as f) from P to Q is said to be one – to – one function, if and only if f (P) = f (Q) then P = Q. In other words every element in Q has only one pre image in element P. One – to – one function diagram is shown below:

According to definition of One to One Function we can say that element of Q has one pre image in element P.
Now we will see One to On...Read More

## Onto

Functions show relationship among Set of input elements and set of outputs elements in such a way that each value of input is matched with exactly one value of output. In other words a relation defined from S to T such that a sub set of S * T is said to be function from S to T.
Now we will see types of function which are given below. There are three types of function.

## Domain

Function displays the relationship between values. Every input term of a function gives back one output value. It is basically written as f (p) where ‘p’ is value you assign to it.
Now we will understand how to calculate the domain in maths? Assume that we have a function and we want to find the domain of function.

All ‘x’ coordinate values of a function are domain of a funct...Read More

## Types of Functions and their Graphs

Function can be used to represent relation between Set of inputs values and set of outputs values in such a way that every value of input is related to exactly one value of output. In other words we can say that relation defined from K to L such that sub set of K * L is called as function from K to L. Let’s see types of Functions and their graphs. The...Read More

## Inverse and Composition of Function

In mathematics the Inverse Function is considered as a function that undoes another function. If ‘g’ is a called a function then the inverse of the function ‘g’ is denoted as g-1.