2. Consider the following functions. Are these ring homomorphisms? If yes, prove it. If no, provide a counterexample. a) f: ZZ given by f(x) = 3x. b) g: R R given by g(x) = x² - c) h: Z→ M(Z) given by h(a) = [ a 8

Q: Prove that the mapping f: G- G defined by f(x) = x-l is an isomorphism of G onto itself.

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Q: (d) Show that g: B → A, g(x) = Vln x is the inverse of f. Why is f-"(x) # -VIn x?

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Q: Give an example of a function h : D4 → GL(2) that is not a homomorphism. Justify your answer.

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A: This is a problem of Abstract Algebra.

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Q: Problem 7 Let He Vam I tudom S = {(2,x) | x E I} CR², dT (81 Ing/ T= {(0,x) | x 1} CR², o ir aut

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