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

\begin{array}{1 1}(A)\;f^{-1}(x)=f(x) & (B)\;f^{-1}(x)=-f(x)\\(C)\;(f\;o\;f) x=-x & (D)\;f^{-1}(x)=\frac{1}{19}f(x)\end{array}
Can you answer this question?
 
 

1 Answer

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Toolbox:
  • A function g is the inverse function $f:R -\{\frac{3}{5}\} \to R $ if
  • $gof=fog=I;g(x)=f^{-1}(x)$
$ f:R -\{\frac{3}{5}\} \to R$
 
$f(x)=\frac{3x+2}{5x-3}$
 
Let $y=\frac{3x+2}{5x-3}$
 
$y(5x-3)=3x+2$
 
$5xy-3y=3x+2$
 
$5xy-3x=3y+2$
 
$x(5y-3)=-3y+2$
 
$x=\frac{3y+2}{5y-3}$
 
we define $g(y)=\frac{3y+2}{5y-3}$ then
 
$fog(y)=f \bigg(\frac{3y+2}{5y-3}\bigg)$
 
$=\frac{3\bigg(\large\frac{3y+2}{5y-3}\bigg)+2}{5 \bigg(\frac{3y+2}{5y-3}\bigg)-3}=y$
 
$=\large\frac{9y+6+10y-6}{15y+10-15y-9}=\frac{y}{1}=y$
 
Hence $g=f^{-1}$
 
and $ f^{-1}(x)=\frac{3x+2}{5x-3}$
 
'A' option is correct

 

answered Mar 5, 2013 by meena.p
 

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