Question:

The mapping f:NN f : N \to N given by f(n)=n3+3,nN f(n) = n^3 + 3, n \in N where N N is the set of natural number, is

Updated On: Jun 23, 2024
  • One to one and onto
  • One to one but not onto
  • Onto but not one to one
  • Neither one to one nor onto
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is B

Solution and Explanation

The correct option is(B): One to one but not onto.

We have, f:NNf : N \to N given by f(n)=n3+3f (n)=n^{3}+3
Let f(n1)=f(n2)f (n_{1})=f (n_{2})
n13+3=n23+3\Rightarrow n^{3}_{1}+3=n^{3}_{2}+3
n13=n23\Rightarrow n^{3}_{1}=n^{3}_{2}
n1=n2\Rightarrow n_{1}=n_{2}
So, f(n)f (n) is one to one mapping 
Let y=f(n)=n3+3y=f (n) = n^{3}+3
n=(y3)1/3\Rightarrow n=(y-3)^{1/3}
Now, yN,nN\forall y \in\,N, n \notin\,N
so, f(n)f (n) is not onto
 

Was this answer helpful?
0
0

Top Questions on Functions

View More Questions

Concepts Used:

Functions

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets, mapping from A to B will be a function only when every element in set A has one end only one image in set B.

Kinds of Functions

The different types of functions are - 

One to One Function: When elements of set A have a separate component of set B, we can determine that it is a one-to-one function. Besides, you can also call it injective.

Many to One Function: As the name suggests, here more than two elements in set A are mapped with one element in set B.

Moreover, if it happens that all the elements in set B have pre-images in set A, it is called an onto function or surjective function.

Also, if a function is both one-to-one and onto function, it is known as a bijective. This means, that all the elements of A are mapped with separate elements in B, and A holds a pre-image of elements of B.

Read More: Relations and Functions