Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
0 votes

Check the injectivity and surjectivity of the function: $f : N\to N\; given\; by\; f(x)\; = x^2 $

$\begin{array}{1 1} \text{injective} \\ \text{surjective} \\ \text{both injective and surjective} \\ \text{neither injective and surjective} \end{array} $

Can you answer this question?

1 Answer

0 votes
  • A function $f: A \rightarrow B$ where for every $x1, x2 \in X, f(x1) = f(x2) \Rightarrow x1 = x2$ is called a one-one function.
  • A function$ f : X \rightarrow Y$ is said to be onto or surjective, if every element of Y is the image of some element of X under f, i.e., for every $y \in Y$, there exists an element x in X such that $f(x) = y$.
  • |x| is always non negative
$ f:N\to N\qquad f(x)=x^2$
Let x and y be two elements in N
For the function f to be injective f(x) =f(y) => x=y
f defined by$ f:N\to N\qquad f(x)=x^2$ is injective
$2 \in N $ there does not exist any x in N
Such that $f(x)=x^2-2$
$\sqrt 2 \notin N$
For every y in N there does not exist an element in N such that f(x)=y
Hence $ f:N\to N\qquad f(x)=x^2$ is not surjective
Hence f is injective but not surjective
Therefore $ f:N\to N\qquad f(x)=x^2$ is injective but not surjective


answered Mar 13, 2013 by thagee.vedartham
edited Feb 28, 2014 by meena.p

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App