ONTO FUNCTION

Example 1 :

Check whether the following function is onto.

f : N → N defined by f(n) = n + 2

Solution :

Domain and co-domains are containing a set of all natural numbers.       

If x = 1, then f(1)  =  1 + 2  =  3.

If x = 2, then f(2)  =  2 + 2  =  4.

From this we come to know that every elements of codomain except 1 and 2 are having pre image with.

In order to prove the given function as onto, we must satisfy the condition.

Co-domain of the function = range 

Since the given question does not satisfy the above condition, it is not onto.

Example 2 :

Check whether the following function is onto.

f : R → R defined by f(n) = n²

Solution :

Domain = All real numbers.

Co-domain = All real numbers.

Since negative numbers and non perfect squares are not having preimage. It is not onto function.

Example 3 :

Check whether the following function are one-to-one.

f : R - {0} → R defined by f(x) = 1/x

Solution :

Domain = all real numbers except 0.

Co-domain = All real numbers including zero.

In co-domain all real numbers are having pre-image. But zero is not having preimage, it is not onto.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.