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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Functions $ f,g:R \rightarrow R $ are defined,respectively,by $f(x)=x^2+3x+1,g(x)=2x-3,$ find\[(i)\quad f\; o\; g\qquad(ii)\quad g\;o\;f\qquad(iii)\quad f\;o\;f\qquad(iv)\quad g\;o\;g\]

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Toolbox:
  • $1.fog$ is defined by
  • $(fog)(x)=f(g(x))$
  • 2.also $gof$ is defined
  • $(gof)(x)=g(f(x))$
Step1:(i)$f,g:R \to R$
 
$f(x)=x^2+3x+1$
 
$g(x)=2x-3$
 
$(fog)(x)=f(g(x))$
 
$=f(2x-3)$
 
$=(2x-3)^2+3(2x-3)+1$
 
$(fog)(x)=4x^2-6x+1$
 
Step2:
(ii)$(gof)(x)=g(x^2+3x+1)$
 
$=2(x^2+3x+1)-3$
 
$(gof)(x)=2x^2+6x-1$
 
Step3:
(iii) $(fof)(x)=f(f(x))$
 
$=f(x^2+3x+1)$
 
$=(x^2+3x+1)^2+3(x^2+3x+1)+1$
 
$(fog)(x)=x^4+6x^3+14x^2+15x+1$
 
Step4:
(iv) $ gog(x)=g(gx)$
 
$=g(2x-3)$
 
$=2(2x-3)-3$
 
$ (gog)(x)=4x-9$

 

 

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

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