Let f be a continuous function on the closed unit disk, analytic on the open disk and zero on tsemi-circle (|z| = 1) ? (=z ? 0 . Show that f is zero. (Consider g(z) = f(z)f(?z).)

Let f be a continuous function on the closed unit disk , analytic on the open disk and zero on the semi - circle ( 2 = 1 ) ( 92 2 0 ) . Show that f is zero . ( Consider 9 ( 2 ) = f ( 2 ) f ( - 2 ) . )