f(x) = (ax+b)/(cx+d) , x is real, x=/= -d/c , b=/=0 , c=/=0

Prove that if

a + d =/= 0

and

(a-d)^2 +4bc = 0

then y=f(x) and y=f^-1(x) intersect at exactly one point

So far I've tried setting f(x) = f^(x) and writing as a quadratic in x. I then tried to find the discriminant and show that it was (a-d)^2 +4bc but I just got into a big mess.

Is this method correct or am I missing something? Is there another approach?