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Homomorphisms, Bijection Map and Continuous Map

1) Prove that the map GIVEN BY is a homomorphism between the real line and open interval (-1,1).

2) Let be the map given by

a) show that f is a bijection map
b) show that f is a continuous map
c) If f a homomorphism? Justify your answer.

Please see the attached file for the fully formatted problems.

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Homomorphisms, Bijection Map and Continuous Map are investigated. The solution is detailed and well presented.

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