Question

f(x)=x-1/x+1,x≠-1 then show that f(f(x)=-1/x given x≠0
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Answer 1

Solution: To prove: f(f(x)) = -1/x or fof(x) = -1/x.

Given, $f(x) = \frac{x-1}{x+1}$

$fof(x) = f(f(x)) = \frac{\frac{x-1}{x+1}-1}{\frac{x-1}{x+1}+1}$

or $fof(x) = f(f(x)) = \frac{\frac{x-1-(x+1)}{x+1}}{\frac{x-1+(x+1)}{x+1}}$

or $fof(x) = f(f(x)) = \frac{x-1-(x+1)}{x-1+(x+1)}$

or $fof(x) = f(f(x)) = \frac{x-1-x-1}{x-1+x+1}$

or $fof(x) = f(f(x)) = \frac{-2}{2x}$

or $fof(x) = f(f(x)) = \frac{-1}{x}$

Hence Proved

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