BY Team Aakash Byju's

Onto Function of Math’s Explained With Examples

Onto Function

The function is said to be onto function if every element of B has at least one or more elements that match with A.

Note: Onto function is also called as surjective function.

Example of Onto Function

Surjection

Not a surjection

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Onto Function

Nicolas Bourbaki introduced this term.

How to find Onto Function: To find the number of onto function from set A with n number of elements to set B with m number of elements.

How to find total number of onto functions?

How to find total number of functions that are not onto?

1. If n < m, then no. of onto functions = 0. 2. If n = m, then no.of onto functions = m!.

Properties of Onto Function

– There is a right inverse for     every onto function. – Function with right inverse     is always a surjective       function. – By composing onto     functions, we get onto     function only.

Example

As a result, every B element has a domain element on A.  Hence it is an onto function.

Let A = {7, 5, 3, 9} and  B = {2, 4} And f={(7, 2), (5, 4), (3, 2), (9, 4)}. Prove f is a onto function?