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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Let $f:R \rightarrow R$ be defined by $f(x)=\Large {\frac{x}{\sqrt{1+x^2}}}$.Then ( f o f o f )(x)=____________.

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  • $(fofof)x=f(f(f(x)))$
$f:R \to R$
 
$f(x)=\frac {x}{\sqrt {1+x^2}}$
 
$ fof=f\bigg(\large\frac{x}{\sqrt {1+x^2}}\bigg)$
 
$=\large\frac{\large\frac{x}{\sqrt {1+x^2}}}{\sqrt {1+\bigg(\frac{x}{\sqrt{1+x^2}}\bigg)^2}}$
 
$=\large\frac{\large\frac{x}{\sqrt {1+x^2}}}{\frac{\sqrt {1+x^2+x^2}}{\sqrt {1+x^2}}}$
 
$=\frac{x}{\sqrt {1+2x^2}}$
 
$f(f(f(1)))=f(\frac{x}{\sqrt {1+2x^2}})$
 
$=\large\frac{\large\frac{x}{\sqrt {1+2x^2}}}{\sqrt {1+\bigg(\frac{x}{\sqrt{1+2x^2}}\bigg)^2}}$
 
$=\large\frac{\large\frac{x}{\sqrt {1+2x^2}}}{\frac{\sqrt {1+2x^2+x^2}}{\sqrt {1+2x^2}}}$
 
$=\frac{x}{\sqrt {1+3x^2}}$
 
$fofof(x)=\frac{x}{\sqrt {1+3x^2}}$

 

 

answered Mar 6, 2013 by meena.p
 

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