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In this paper we present a new method of determining Koebe domains. We apply this method by giving a new proof of the well-known theorem of A. W. Goodman concerning the Koebe domain for the class T of typically real functions. We applied also the method to determine Koebe sets for classes of the special type, i.e. for T M;g = {f ε T : f(δ) Mg(δ)}, g ε T S, M > 1, where δ = {z ε C: |z| < 1} and T, S stand for the classes of typically real functions and univalent functions respectively. In particular, we find the Koebe domains for the class TM of all typically real and bounded functions, and for the class T(M) of all typically real functions with ranges in a given strip.
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