Explanation

(c)
$\ f\left\lbrack f\left( f(x) \right) \right\rbrack = f\left\lbrack f\left( \frac{1}{1 - x} \right) \right\rbrack = f\left( \frac{1}{1 - \frac{1}{1 - x}} \right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$
$\left\lbrack \because f(x) = \frac{1}{1 - x} \right\rbrack$
$= f\left( \frac{1 - x}{- x} \right) = \frac{1}{1 + \left( \frac{1 - x}{x} \right)}$
$\Rightarrow \ f\left\lbrack f\left( f(x) \right) \right\rbrack =$ $x$
$\therefore\ \$ The derivative of composite function is equal to 1.