(Properties of the inverse image of functions and continuity) Let f: C C be any function,...

 

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(Properties of the inverse image of functions and continuity) Let f: C C be any function, show that for any A, B ≤C 1. f¹(AUB) = f¹(A)uf-¹(B) 2. f¹(An B) = f'(A) nf-¹(B) 3. f¹(A) = f¹(B) if A = B 4. f¹(AB) = f¹(A) f¹(B) where f¹(D) = {z € C: f(z) e D} and Z\D = {z € Z: z D} (Properties of the inverse image of functions and continuity) Let f: C C be any function, show that for any A, B ≤C 1. f¹(AUB) = f¹(A)uf-¹(B) 2. f¹(An B) = f'(A) nf-¹(B) 3. f¹(A) = f¹(B) if A = B 4. f¹(AB) = f¹(A) f¹(B) where f¹(D) = {z € C: f(z) e D} and Z\D = {z € Z: z D}