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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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State whether the function is one-one, onto or bijective.

$f : R\; \to R$ defined by $f(x)\; =\; 1+x^2$

$\begin{array}{1 1} \text{neither one -one nor onto} \\ \text{bijective} \\ \text{only one-one} \\ \text{only onto}\end{array} $

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1 Answer

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Toolbox:
  • A function is one-one
  • if $f(x)=f(y) => x=y$
  • function is onto. if then exist x such that for $f(x)=y $ foe every y
  • Bijective if both one-one and onto
$ f: R \to R \qquad f(x)=1+x^2$
 
$x_1\,x_2 \in R $
 
$f(x_1)=f(x_2)$
 
$=>1+x_1^2=1+x_2^2$
 
$x_1^2=x_2^2$
 
$x_1=\pm x_2$
 
This is not imply $x_1=x_2$
 
f is not one one
 
Also $f(1)=f(-1)=2$
 
but $1=-1$
 
so f is not onto
 
Hence f is neither one-one nor onto
 

 

answered Mar 6, 2013 by meena.p
 

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