Table of Contents

## Onto Function

Onto Function – Infinity Learn:

- An onto function is a function that assigns a unique output to every input, and every input corresponds to a unique output.
- Onto functions are mathematical functions that can be used to describe relationships between elements in a set. They are used to determine if a given element is a member of a set, and to find the successor and predecessor elements of a given element. The most common onto function is the function that determines if a given element is a member of a set. This function is usually represented by the symbol “x” in mathematical notation.

## What is a Function?

A function is a set of ordered pairs (x, y) where each x corresponds to a unique y. The function assigns a unique output to every input.

## Types of Functions

There are many different types of functions, but some of the most common are polynomial functions, exponential functions, and logarithmic functions.

- A polynomial function is a function that can be represented by a sum or a product of terms, where each term is a monomial (a product of a constant and a variable). The degree of a polynomial function is the largest degree of any of the terms in the function.
- An exponential function is a function in which the value of the function increases or decreases at a rate that is proportional to the current value of the function.
- A logarithmic function is a function in which the value of the function increases or decreases at a rate that is proportional to the logarithm of the current value of the function.

## What is Onto Function?

Onto function is a function that maps objects in a given domain to objects in a given range.

## Properties of Onto Mapping

- A mapping is a one-to-one correspondence between two sets, usually denoted by an equation. The function that defines the mapping is a bijection.
- The inverse of a mapping is a function that “undoes” the mapping. The inverse is usually not a bijection, but it is a function.
- A mapping is injective if every element in the domain is mapped to a unique element in the range. A mapping is surjective if every element in the range is mapped to an element in the domain. A mapping is bijective if it is both injective and surjective.

## Relationship between Function and Domain

A function is a mathematical relation between two sets, usually denoted by an equation. The function assigns a unique output to every input. The domain is the set of all inputs to the function, while the range is the set of all outputs.

## Numbers of Onto Functions

- There is no definitive answer to this question as it depends on the specific application.
- However, in general, there are many more possible onto functions than there are specific sets.