Explanation

(a)
Given, $f(x) = \frac{ax + b}{cx + d}$ and $fof(x) = x$
$\Rightarrow \ \ \ \ \ \ \ \ \ f\left( \frac{ax + b}{cx + d} \right) = x$
$\Rightarrow \ \frac{a\left( \frac{ax + b}{cx + d} \right) + b}{c\left( \frac{ax + b}{cx + d} \right) + d} = x$
$\Rightarrow \ \ \ \ \ \frac{x\left( a^{2} + bc \right) + ab + bd}{x(ac + cd) + bc + d^{2}} = x$
$\Rightarrow \ \ \ \ \ \ \ \ d = - a$