Question

$f(x) = x - 1 \div x + 1.then \: find \: f(f(x))$
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Answer 1

$\large\underline{\sf{Solution-}}$

It is provided that

$\rm :\longmapsto\:f(x) = \dfrac{x - 1}{x + 1}$

$\rm :\longmapsto\:f\bigg(f(x)\bigg)$

$\rm \: = \: f\bigg(\dfrac{x - 1}{x + 1} \bigg)$

$\rm \: = \: \dfrac{\dfrac{x - 1}{x + 1} - 1}{\dfrac{x - 1}{x + 1} + 1}$

$\rm \: = \: \dfrac{\dfrac{x - 1 - x - 1}{x + 1}}{\dfrac{x - 1 + x + 1}{x + 1}}$

$\rm \: = \: \dfrac{ - 2}{2x}$

$\rm \: = \: \dfrac{ - 1}{x}$