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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective:$(ii)\quad g(x)\;=\;|\;x\;|$

Note: This is the 2nd part of a  4 part question, which is split as 4 separate questions here.

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  • 1.A function f on set A is one-one ie $f(x)=f(y)=>x=y \qquad x,y \in A$
  • 2.A function f on set A is onto if for every $y \in A$ than exist $ x\in A$ such that $f(x)=y$
  • 3.A function is bijective if it is both one-one and onto
(ii)$g(x)=|x| \qquad a \in [-1,1]$
 
Let $x_1=-1\;and \; x_2=1$
 
$g(x_1)=|-1|=g(x_2)|1|=1$
 
but $x_1 \neq x_2$
 
Hence g is not a one one function
 
Consider y=-1 we cannot find any no. $ x \in A$ such that $g(x)=y=-1$
 
modulus of a number is always positive
 
Therefore g is neither one -one nor onto

 

 

answered Mar 4, 2013 by meena.p
 

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