Let φ: ℤ→ℤ defined by φ(x) = x + 2. Show φ is a homomorphism.

Q: 7. Prove that the function f:Z → Z defined by f (x) = x + 8 is one-to-one and onto.

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Q: Let x = [2] Show that the transformation T defined by T(x) = Edit Insert Formats BI Ụ X, xỉ A 블로 N H…

A: We will show that the given transformation is not Linear.

Q: Let f: IR → R and g: R → R with f(x) = 5x – 7 and g(x) = x2 – 4x + 4 Find: a) Domain of . g(D(f.g))…

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Q: Let C = {0, 1, 2, 3} and f: C → C, g: C → C with ƒ = {(0, 2), (1, 2), (2, 3), (3, 0)}, {(0, 3), (1,…

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Q: Show that the linear transformation is continuous at every Xo = R³. F(X) = x₁ + x2 + x3 2x13x2 + x3…

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Q: evalieante the folliwing innegratin ni fullowing dif Path C I'm 2 fo,1). (3,!) -3 -2 -1' pathz path!…

A: The given problem is to check that the given is satisfying the cauchy reimann equations or not and…

Q: Prove that there is an additive function T : R --> R that is not linear.

A: Let T: V→W  be the linear transformation and we it is linear,…

Q: Let T: P2 → P2 be defined by T(p(x)) = xp'() A. Describe the kernel of T. B. Describe the range of…

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Q: The mapping L(x) = ax + b is linear. ihi O

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Q: Let f R2 R² be an isomorphism where : → ƒ ( [¹³]) = [()] and ƒ ([×4]) = }}] Find(G)

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Q: Let ƒ: R² → R² be an isomorphism where ([-])-[²] and f([:]) = [] = Find f ¹ƒ( [7¹]) X 0 2 2 0

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Q: 1. Define f : (- o, 2) → (- 0, 1) by f(x) = . Show that f is bijective. x+1 *-2

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Q: Show that f: R\{2} → R\{5} defined by f(x) = (5x+1)/(x - 2) is bijective.

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Q: Let X = {a, b, c, d,e} and let T = {X, Ø, {a}, {a,d}, {a,e}}, then * O (X,T) is not connected but it…

A: No information is given for topology on Y So i have solved only the middle question

Q: Let the function f: R R be defined by f(r) = 3r -5. Prove that the function is bijective.

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Q: Prove that the function : R-{1} →R- {2} defined by 2a f(x)= s bijective. 2 1

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Q: The function f : R → R defined by the formula f(x) = 3x − 5 for all x ∈ R was shown to be one-to-one…

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Q: Show that U(8) is isomorphic to U(12).

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Q: Show that the mapping f:R2 → R² defined by f(x1, x2) 5x2) is linear. = (2x1 + x2, -3x1 +

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Q: Prove that the mapping f : U(16) ---> U(16) given by f(x) = x^5 is an automorphism.

A: The given map is f:U16→U16 defined by fx=x5. We have to prove that f is an automorphism. We know…

Q: b) Find 4°f(x) if f(x) = (3x+1)(3x+4)(3x+7) ... (3x + 19) %3D

A: We will answer the first question only as we don't answer multiple question at a time. Please…

Q: Exercise 2. Let f : A → B be a function with Y1 and Y2 subsets of B. Prove that if Y1 C Y2, then…

A: Let f:A→B be a function and let Y1,Y2⊆B. Suppose that Y1⊆Y2 To show f-1(Y1)⊆f-1(Y2) Let x∈f-1(Y1)…

Q: 3x +1 III.(10) Prove that the function f: R – {5} –> R – {3} defined by f(x) = is a bijection. x- 5

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Q: Write restiction(s) for input of each if any. Assume g(x) is defined everywhere.

A: 1) A polynomial function is defined for all values of x. So, this function does not have any…

Q: Show that the function f : R – {3} → R – {5} defined by f(x) = is bijective and determine f-'(x) for…

A: The given function is                                f : ℝ-{3}→ℝ-{5} defined by…

Q: Let T and U be two transformations. What does the composition  T∘U mean?

A: Here T and U are transformation, the composition is explained below see the explanation below.

Q: Let L be a linear transformation from P₂ → R2x2 such that L(f) — ƒ(1) 0 Find dim[Range(L)] ƒ(2)…

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Q: The cyclic rule is a sometimes useful identity that applies to the situation in which three…

A: We have to show that