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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Let $f:R\rightarrow R $ be defined by $f(x)=3x^2-5\; and \;g:R\rightarrow R \;by \;g(x)=\Large {\frac{x}{x^2+1}}$.Then g o f is

\begin{array}{1 1}(A)\;\frac{3x^2-5}{9x^4-30x^2+26} & (B)\;\frac{3x^2-5}{9x^4-6x^2+26}\\(C)\;\;\frac{3x^2}{x^4+2x^2-4} & (D)\;\frac{3x^2}{9x^4-30x^2-2}\end{array}

Can you answer this question?
 
 

1 Answer

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Toolbox:
  • $f:R \to R$
  • $g:R \to R$
  • $(gof)(x)=g(f(x))$
Given $f:R \to R$
 
$f(x)=3x^2-5$
 
$g:R \to R$
 
$g(x)=\frac{x}{x^2+1}$
 
$(gof)(x)=g(3x^2-5)$
 
$=\frac{3x^2-5}{(3x^2-5)^2+1}$
 
$=\frac{3x^2-5}{(9x^4-30x^2+26}$
 
'A' option is correct

 

 

answered Mar 5, 2013 by meena.p
edited Mar 27, 2013 by meena.p
 

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