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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Find \( gof\) and \(fog\), if (i) \( f(x) = |\;x\;| \, and \, g(x) = |\;5x-2\;| \)

Note: This is part 1 of a 2 part question, split as 2 separate questions here.
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  • Let f,g, be two functions, the composition of functions gof is defined by, $(gof)(x) =g(f(x))$
  • Let f,g, be two functions, the composition of functions fog is defined by, $(fog)(x)=f(g(x))$
(i)
 Let the function f and g be defined by
 
$f(x)=|x| \qquad g(x)=|5x-2|$
 
Then,$(gof) (x)=f(g(x))$
 
$=g(|x|)$
 
Therefore gof (x) $ =|5|x|-2|$
 
We also see that, $(fog)(x)=f(g(x))$
 
$=f(|5x-2|)$
 
$ =\bigg||5x-2|\bigg|$
 
since we know that for any y,$||y||=|y|$
 
therefore we see that fog(x) $= |5x-2|$
 
 

 

 

answered Feb 25, 2013 by meena.p
edited Mar 19, 2013 by thagee.vedartham
 

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