Question

If $f\left(x\right)=\frac{1}{(1-x)}$ find $\left(fofof\right)\left(x\right)=?$

Answer 1

$f\left(x\right)=\frac{1}{1-x},f0f0f0\left(x\right)$

$f0f0f0\left(x\right)\Rightarrow \frac{1}{1-\frac{1}{1-\frac{1}{1-x}}}$

$\Rightarrow \frac{1}{1-\frac{1}{\frac{(1-x)-1}{1-x}}}$

$\Rightarrow \frac{1}{\frac{1-(1-x)}{-x}}\Rightarrow \frac{1}{\frac{-x-(1-x)}{-x}}$

$\Rightarrow \frac{-x}{-x-1+x}$

$\Rightarrow \frac{-x}{-1}=x$

$\therefore f0f0f0\left(x\right)=x$