Question

If $f\left(x\right)=\frac{1}{1-x}$, then $\left(fofof\right)\left(x\right)$ is

Answer 1

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

Now,

$\left(fofof\right)\left(x\right)$

$=\left(fof\right)\left(f\right(x\left)\right)$

$=\left(fof\right)\left(\frac{1}{1-x}\right)$

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

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

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

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

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

$=x$.