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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Let f : $R \to R$ be the function defined by $f(x)=2x-3$ $\forall x \in R$.Write $f^{-1}.$

$\begin{array}{1 1} \large\frac{x-3}{2} \\\large\frac{2x}{3} \\ \large\frac{3x}{2} \\ \large\frac{x+3}{2} \end{array} $

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  • $f:R \to R; $ A function $g:R \to R $ is inverse of f if $fog=I_R=gof$ when I is the identify function
$ f:R \to R ; f(x)=2x-3$
 
we define a function
 
$y:R \to R$
 
Let y be an arbitary element of range f
 
$y=2x-3$
 
$=> x=\frac{y+3}{2}$
 
Let $g(y)=\frac{y+3}{2}$
 
$(gof) (x)=g(f(x))=g(2x-3)$
 
$=\frac{2x-3+3}{2}$
 
=x
 
Also $ (fog)(y)=f(\frac{y+3}{2})$
 
$=2(\frac{y+3}{2})-3$
 
=y
 
Hence g is in inverse of f
 
and $f^{-1}(x)=g(x)=\frac{x+3}{2}$

 

 

answered Mar 1, 2013 by meena.p
 

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