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  4. Let f(x)= (x-1/x+1) then f(f(x)) is

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Q. Let $f(x)= \frac{x-1}{x+1}$ then $f(f(x))$ is

Relations and Functions - Part 2

Solution:

$f(f(x))=\frac{f(x)-1}{f(x)+1}=\frac{\frac{x-1}{x+1}-1}{\frac{x-1}{x+1}+1}$
$= \frac{x-1-x-1}{x-1+x+1}=\frac{-2}{2x}=\frac{-1}{x}$