Find the kernels and images of the following homomorphisms. Which of the homomorphisms are injective? Which are surjective? (i) The mapping 0 : Z₁₁ → Z₁ given by 0(x) = x². (ii) The mapping ☀ : R* → R* given by o(x) = x³. (iii) The mapping : G → G given by y(x) = g-¹xg for x E G where G is a group and g € G. (You may assume that this is a homomorphism.)

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: Which are invertible

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Q: Find the kernels and images of the following homomorphisms. Which of the homomorphisms are…

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A: Step 1:na Step 2: Step 3: Step 4:

Q: (3) Conjugate the map f(x) = 2x² +x – 3 to a map of the form Q(x) = x² + c. Find the conjugacy map h…

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Q: Consider the map: n+1 = f(xn). If ƒ(ƒ(ƒ(ƒ(ƒ(x))))) − x = 0, which statement below is unequivocally…

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Q: Construct a nontrivial homomorphism $: Zg → Zı5 >

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Q: Let T: RR∞ be defined by T(x₁, x2, 3,...) = (0, x₁,x₂,...) (a) Using the definition of linear…

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Q: Determine if the map g : Q ! Q dened by g(x) = x/(x2+1) is one-to-one.

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