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Many One Function

Many one function is an important function which relates two or more elements of the domain set with a single element of the codomain set. Many one function is a function f: x→ y such that two or more elements of the set x are related to a single element of the set y.

Let us learn more about many one function, properties of many one function, with examples, FAQs.

1.	What Is Many One Function?
2.	Properties Of Many One Function
3.	Examples On Many One Function
4.	Practice Questions
5.	FAQs On Many One Function

What Is Many One Function?

Many one function is a function in which two or more elements of a set are connected to a single element of another set. The function f: x → y, such that two or more elements in the domain of the function f and belonging to the set x are connected to a single element in the codomain of the function f and belonging to the set y. Here two or more two elements of the domain are connected with the same element in the codomain.

Let us consider an example with two sets with the set A = {1, 2, 3, 4, 5} as the domain, and the Set B = {x, y, z} as the range. Here the function f from A to B is said to be many one function, if we have f = {(1, x), (2, x), (3, x), (4, y), (5, z)}.

The many one functions can also be called a constant function if all the elements of the domain are connected to only one element in the codomain. And the many one function is called an onto function if each element in the range has been utilized.

Properties Of Many One Function

The following are some of the important properties of many one function.

The domain of the function should have at least two elements having the same codomain value.
The number of elements in the domain of many one functions is more than the number of elements in the codomain.
The codomain of the many one functions has the same value for more than one domain value.
The codomain of many one functions is always lesser than the range value.
The many one function can also be called a constant function if there is only one codomain.

Related Topics

The following topics help in a better understanding of many one functions

Examples on Many One Function

Example 1: Find the domain and range of the many one function f = {(1, a), (2, a), (3, a), (4, b), (5, b), (6, c)}

Solution:

The given function is f = {(1, a), (2, a), (3, a), (4, b), (5, b), (6, c)}

Here we have:

Domain = (1, 2, 3, 4)

Range = (a, b, c)

We observe that the elements 1, 2, 3, in the domain are all connected to the same element 'a' in the range set. Hence we see that this function connecting the elements of th domain set to the element in the range set, makes a many one function.

Therefore, the given function is many one function.
Example 2: Prove that the function f(x) = x² is an onto function.

Solution:

The given function if f(x) = x². Let us take a few values for the domain of this function and find the range, and then try and understand the type of this function.

Let x = 2, f(2) = 2² = 4

For x = -2, f(-2) = (-2)² = 4

x = 3, f(3) = 3² = 9

x = -3, f(-3) = (-3)² = 9.

For the elements of x = 2, -2, the f(x) value is 4, and for the values of x = 3, -3, the range is 9.

Therefore, the function f(x) = x² is a many one function.

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Practice Questions on Many One Function

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FAQs on Many One Function

What Is Many One Function?

Many one function is a function that connects two or more elements of the domain set with a single element in the range set. For a function f: x → y, two or more elements of the domain set x, are connected to a single set y. The number of elements in the domain in a many one function is more than the number of elements in the codomain set.

How To Find The Range Of Many One Function?

The range of the function are the elements of the codomain set, which has been connected to two or more elements of the domain set. For a function f: x→y, the elements of the set y is the range of the many one function, in which two or more elements of the set x have been connected to a single element in the set y.

What Is The Domain Of Many One Function?

The domain of many one function is the set of elements from the domain set, which have been connected to two or more elements of the codomain set. The function f: x → y has the elements of the set x as the domain set, in which two or more elements of the set x are connected to a single element in the range set y.

Give Example Of Many One Function?

An example of the many one function is the set A = {1, 2, 3, 4, 5} as the domain, and the Set B = {x, y, z} as the range. Here the function f from A to B is said to be many one function, if we have f = {(1, x), (2, x), (3, x), (4, y), (5, z)}.

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