Ask Questions, Get Answers

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

Let $A=[-1,1].$ Then,dicuss whether the following functions defined on $A$ are one-one,onto or bijective:$\; f(x)\;=\;\frac{x}{2} $

Note:This is the 1st part of the 4 part question
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 or injective 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 $f(x) = y$.
  • A function is bijective if it is both one-one and onto
Given $f(x)=\frac{x}{2}\qquad x \in [-1,1]$
Let $f(x)=f(y)$
Step1: Injective or One-One function:
=>$ \frac{x}{2}=\frac{y}{2}$
f is one one
Step 2: Surjective or On-to function:
$ 2 \in [-1,1]$
There does not exists an element n in A
Such that $f(x)=y\qquad \;for\;y=1$
Therefore f is not onto
Solution:Hence f is one-one but not onto



answered Mar 4, 2013 by meena.p
edited Mar 27, 2013 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