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if $f(x)=\frac{x-1}{x+1}$ , x∈R-{-1}, then f-1(x) is equal to

 

$a. \frac{x-1}{x+1} b.\frac{x+1}{x-1} c.\frac{2}{1+x}$ d.Does Not exist

asked in Graph Theory by Veteran (14.4k points)  
edited by | 68 views

1 Answer

+3 votes
Best answer
  • $f(x)=\frac{x-1}{x+1}$ , here f(1) = 0
  • By assigning $x = 0$ in the given options , none of them results $1$
  • So, it should be none of these gievn options for inverse. And f(x) can never be equal to 1 and $f^{-1}(x)$ does not exist for -1

 

$\begin{align*} &\Rightarrow\frac{y}{1} =\frac{x-1}{x+1} \\ &\Rightarrow \frac{y-1}{y+1} =\frac{(x-1)-(x+1)}{(x-1)+(x+1)} \\ &\Rightarrow\frac{y-1}{y+1} = \frac{-2}{2x} \\ &\text{x and y are dummy only} \\ &\Rightarrow f^{-1}(x) = \frac{1+x}{1-x} \\ \end{align*}$ 

answered by Veteran (41.3k points)  
edited by
sorry! 4th option is doesn't exist. what is your answer (D) or b

f-1(x) does not exist for x=1
so option D is correct..

Awesome! you're right f^-1(x) doesn't exist for 1.
this $\frac{x-1}{x+1}$ fraction  can never be equal to one !
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