Let f: C→ Cbe a holomorphic function. Assume there is a ro > 0 such that |f(2)| < |z|? for |2| > ro- (i) Show that f(3) (2) = 0 for all z E C. (ii) Show that f is a quadratic polynomial.

Q: Q7; Functions (a) Prove that the function f : Z4 → Z12 given by f(T) = [3x] is well %3D defined.

A: we need to prove homomorphism

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Q: 1) Find the domain of the real-valued function given below 3 f(x) = VT – 2

A: Given that: f(x)=x-3x-2

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A: We will use the basic knowledge of ring theory to answer this question properly, in detail.

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Q: 3. (a) Prove that the function f : R → R, ƒ(x) = 4x² −14x¹+30x-17, is injective. (b) Find the…

A: The answer to this question is given below.Explanation:

Q: Let f: Z → Z be defined by f(x) = x² + 1, and let C = {1,2,3}.

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A: We shall use the intermediate value theorem to answer this question

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A: To prove that the given conditions on the analytic function force it to be the constant function…

Q: ƒ(X) e F[X] be a non-constant polynomial of degree d. Prove that f(a) has degree at least over F.

A: ANSWER :

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A: Here we have to find the maximum and minimum value of the given function.

Q: Prove that f(x) = x³ + x/2 is C¹-structurally stable.

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