prove that if g is an automorphism of the unit disc, then there exist real numbers a,b,c,d such that ad - bc = 1 and so that for any z

16. Let f (2 ) = 2 - 2 .1 - w itz and f-1(w) = i 1 + w (a) Given 0 E R, find real numbers a, b, c, d such that ad - bc = 1, and so that for any z E H az + b cz + d = f-1 (eof (z) ) . (b) Given o E D find real numbers a, b, c, d so that ad - bc = 1, and so that for any z E H az +b cz + d -1 ( ralf ( = ) ) ) , with va defined in Section 2.1. (c) Prove that if g is an automorphism of the unit disc, then there exist real numbers a, b, c, d such that ad - bc = 1 and so that for any z E HI az+b cz + d logof(z). [Hint: Use parts (a) and (b).]