Question

Suppose f is analytic on a bounded domain D and is continuous up to
and on the boundary of D.

If f does not vanish, show that IfI attains its minimum on the boundary
of D. [Apply the Maximum Principle to the reciprocal of f.]

Answer 1

This one is tricky, since f does not vanish 1/f is also analytic and takes its maximum on the boundary D

Answer 2

are you supposed to prove the maximum modulus theorem or just apply it?

Answer 3

just apply it

Answer 4

then consider
\[\frac{1}{f}\] and be done i think

Answer 5

a maximum of 1/f is a minimum of f

Answer 6

oh you write the answer already. sorry

Answer 7

thanks for the help though