In a problem I was asked to find the domain of
f of f, which is f(f(x))
where f(x)=(ax+b)/(cx+d)
so I get: f((ax+b)/(cx+d))
(a)(ax+b)/(cx+d)
(c)(ax+b)/(cx+d)
after I multiply it out I get
(a^2x+ab+bcx+bd)/(cx+d)
(cax+bc+cdx+d^2)/(cx+d)
now the "cx+d" cancels and you are...